The first thing to note is that Christianity came to the British isles a couple of hundred years before the various tribes who'd become the English (who we tend to refer as Anglo-Saxons, as those were two of the larger groups) arrived. The first Christians in Britain were Romans, probably in the 2nd or 3rd centuries, though they were very much a minority. By the time the Romans Empire finally left Britain in 410, Rome was an officially Christian Empire... but had only been so for 20 years. Christianity had been growing quickly throughout the 4th century, but it's difficult to tell how much this affected Britain. Certainly, there were Christians in Britain, but by 410 were they a majority? Were they almost everyone? It's very difficult to tell.

So, pre-Christian names would be Celtic or Roman names, but I don't know enough about them to give a good answer.

But since you mentioned English people, I wondered if you were more interested in what kind of names people in Britain had before Christian names became popular. The fashion for Biblical names only really took off in the early 2nd millenium (mixed with a few Norman names of Germanic origin, of course). If you look at the name Thomas, for example (after Jesus' disciple Thomas), it's incredibly common in the 16th century, but hardly found at all in the 8th century. There are Biblical names before 1000, (for example, Saint David of Wales), but they're less common than "traditional" local names. In fact, in a list of 89 Anglo-Saxon saints' names there's about 3 Biblical names (John, Paulinius, another John). For some examples of Anglo-Saxon names prior to Christian names becoming fashionable, a good set of examples would be the House of Wessex, Kings of south-west England and later all England, starting in the late 8th century AD. They include names like: Aethelbard, Aethelbert, Alfred, Edmund, Edgar, Edward, Aethelstan, Ethelred. They ended up being succeeded by Harold Godwinson. Or, the Kings of Northumbria, in north-east England, who included names like Aethelfrith, Oswald, Osric, Edwin, Oswiu. (I should say that Aeth means "noble", and so probably was less common amongst normal people.)

These are just a few examples, of course there were hundreds of English names. One thing I hope you note from the above is that a small portion of these names have survived, such as Edward, Edgar, Alfred, Oswald, Cuthbert, etc. Some examples of Anglo-Saxon girls names that survive include Audrey, Edith, and Mildred.

But there are hundreds of other Anglo-Saxon names that you will hardly ever find in Britain today. My middle name is Oswin, but I've only ever met one other Oswin (my grandfather, who I'm named after).

Welsh names were completely different of course. Due to attempts by the Welsh to maintain their own distinctive (non-English!) names, you can still find a fair few Rhodris, Llewellyns, or Owains, today, names found amongst Welsh people during the 1st millenium. But I think today you'd be hard pressed to find a Llywarch, Dyfnwallon, or Hyfaidd. Of course, none of these are anywhere near as common in Wales as David, Dave, Davis, Davies, etc!

I'm afraid I don't know enough about Anglo-Saxons give you an answer about that which is up to this sub's standards. I can tell you they didn't use Mc or Mac. The Welsh sometimes (but not always!) used the particle "ap", meaning son of, like Rhodri ap Hyfaidd, King of Dyfed in the 10th century, son of Hyfaidd ap Bledrig.

Just for clarification do you mean pre 3rd century during the Romano-British time? Or do you mean the early Anglo Saxons?