Here is a page by Regia Anglorum exploring the colours available using natural dyes available in Anglo-Saxon England. The picture at the top is a good visual of the vibrancy of colours available.

A few years back I did an analysis of the colours and fabrics mentioned in various sailors' wills and probate inventories. Obviously it all relates to one occupational group, but it does give the lie to the idea that common people all wore drab clothes in the early-modern period. It's also out of period for the OP, but the technology and cost of dyeing didn't change dramatically, so it perhaps has some relevance. Here is what I wrote then:

"I have been tabulating the colours and fabrics mentioned in various sources describing sailors' clothing of the 17/18th centuries (up to 1750). More often than not the garments are only listed, without description, but there are still plenty of more detailed descriptions available which might be enough for us to draw some conclusions about colours and fabrics. What follows is information culled from a variety of sources (listed more fully at the end), and some general points need to be made. I have ignored any mention of clothing which does not also list either fabric or colour. Most descriptions list fabric or colour, only a few list both. The information comes principally from 3 sources: probate inventories or similar lists of possessions, runaway adverts, and the inventory of a london slop-shop. I have deliberately not included the '6 dozen worsted and threed stockens, 3 dozen of speckled shirts and Breaches' which were sent by Frederick Phillipse to supply the Madagascar pirates in 1693, because so many unvaried items from a single source would, I feel, unrealistically skew the proportions. For the same reason I have not included any slop clothing supplied to RN ships under the Admiralty slop contracts (which are well discussed elsewhere in any case).

In this study a sample of the following numbers of garments has been used: 161 jackets and coats, 89 waistcoats, 41 'frocks' or smocks, 140 pairs of breeches, 11 pairs of trousers, 173 shirts, and 20 pairs of stockings. Because I have not included undescribed articles of clothing in this sample it cannot be used to establish the relative prevalence of any type of garment. For example, breeches are usually accompanied by a description of fabric or colour, while trousers are not: the sources I have used contain many more than 11 pairs of trousers, so the actual ratio of breeches to trousers in the sources is not 140-11.

**COLOURS

Jackets** 44 blue 21 striped 8 white 7 brown 5 grey 4 'light coloured' 3 'dark' 3 green 2 red 2 black 1 'sad coloured' 1 'plaid' 1 'floured'

Waistcoats 8 white 6 red 3 blue 2 brown 2 black 1 striped 1 'coloured' 1 green 1 'drab'

Frocks 6 blue

Breeches 27 striped 7 blue 5 brown 2 white 2 black 1 'dark' 1 grey 1 'light' 1 olive

Trousers 6 striped

Shirts 82 striped 35 white 13 blue 10 check 5 speckled

Stockings 7 pr white 3 pr grey 2 pr blue

**FABRICS (I appreciate that fabric-types fall outside the scope of the OP, but I'm going to leave them in for the sake of completeness)

Jackets 30 fustian 25 canvas 5 kersey 3 flannel 2 broadcloth 1 serge 1 drugget 1 duffel

Waistcoats 28 cotton (cue the arguments about 'cotton') 14 ticking 10 fustian 8 kersey 6 flannel 1 silk 1 camlet 1 nankeen 1 holland

Frocks 20 fustian 15 canvas

Breeches 28 canvas 28 ticking 17 fustian 11 linen 7 'woollen' 5 kersey 4 leather 2 broadcloth 1 worsted 1 camlet 1 drugget

Trousers 3 fustian 1 canvas 1 linen 1 cotton

Shirts 27 holland 1 dowlas 1 osnabrig

Stockings 6 worsted 5 yarn 1 jersey 1 thread

Sources The inventory of Joseph Haycock's slop shop, 1699 (London Metropolitan Archives, Orphans Inventory 2330). Probate records from Records and Files of the Quarterly Courts of Essex County, Mass., vols v-ix (1672-1686); Probate Inventories of Port Royal, vols 2(1679-1686), 3 (1686-1694), 10 (1712-1716); miscellaneous collected probate inventories, mostly from the National Archives, Kew, PROB series. Runaway advertisements, from London newspapers 1700-1730, and colonial newspapers 1720-1770. 'Account of clothes &c. sold at the mast of HMS Gloucester, belonging to James Bearcroft, Gunner, D.D., 14 March 1750', in The Naval Miscellany, vol. II (NRS), pp. 289-291."

It would depend on the colour and also how the nature of the dye. Some dyes (like that in jeans) aren't chemically bound (covalent bonding) to the material but instead 'sits on' the material. Which is why, if you've ever worn converse and new dark denim jeans you end up with blue tipped converse. The lack of 'colour-fastness' and susceptibility of the dye to light can affect how we see older clothing today.

Although, that said, woad is pretty vibrant but I'm unsure as to how colourfast it is.

I've seen that is older than the mid-19th century has fairly dull colors. I assume that this is partly due to aging and fading

This is not necessarily the case as if I recall correctly azo dyes weren't discovered until 1850ish. The Azo dyes are very vibrant and also had the added bonus of chemically colourfast compared to the older dyes. We can also make a huge range of colours with azo dyes so compared to clothes at the time they'd seem pretty colourful.

I think I remember from chemistry class that there's a portrait of Napoleon's wife Eugiene with a green Azo dyed shawl/cloak but I can't remember for the life of me which one it is.

Still, a clothes historian could probably give a much better description than me but I hope this helps a little.

Take a look at paintings from the 14th and 15th centuries. While the colors have faded somewhat, oil paints that use mineral dyes tend to hold their colors better over a period of centruies compared to the vegetable dyes that were largely used for fabric right up until the mid-19th century.
Take a look at the paintings in in the U.S. National Gallery of Art, from the 13th and 14th centuries. Although these are mostly religious subjects, the figures are clothed in what are essentially contemporary styles -- the idea of making the past look different from the present didn't appear in Western Art until sometime in the 15th century.

Notice especially Paolo Veneziano's The Coronation of the Virgin painted in 1324. Even more than seven centuries later, the reds and yellows are still vibrantly bright.

Keep in mind that most fabric dyes used before the mid-19th century were organic vegetable vegetable dyes. The had bright colors when new, but were much less colorfast than modern analine dyes and would fade rabidly if washed too often or exposed to sunlight for an extended period of time.