I am neither an expert in Royal Navy nor the general 18th century navy, but can anyway tell you bow and stern mounted guns (not sure if exactly fit the definition of chasers, but definetly pointing forward and backwards) appear frequently and were quite usual in 16th and 17th century at least. Certainly not the case that nobody thought of them until 1800.

In fact, if you expand your view to include galleys, their main armament were bow mounted guns example since the 15th century. For sailing ships, caravels are currently considered to have one larger caliber piece in the bow, which could be then maneuvered into position and fired (here is a poor quality image where you might be able to make out the piece in the front ).

As for the larger sailing ships there are many images of ships having stern "chasers", and much less, but a few showing some with front facing guns. Let's collect some.

Examples of stern guns (sticking to the 16th century):

• The Embarkation of Henry VIII at Dover - 1540
• Anonymous (lisbon) - 1530s
• Portuguese Carracks off a Rocky Coast - 1540
• Pieter Brueghel 1 - mid 16th century
• Pieter Brueghel 2 - mid 16th century
• Henry Grace a Dieu, English Anthony roll, 1546
• French carrack 1548
• Adriaen Collaert - 1582
• Theodore de Bry (Lisbon / Flanders) - 1592
• anonymous (Amsterdam) - 1594

Examples of bow guns (upto end of 17th century):

• Grand Mistress, English Anthony roll, 1546
• French caravel 1548
• Pieter Brueghel 3 - mid 16th century
• Portuguese caravel 1590s
• Hendrick Cornelisz Vroom - 1617
• Alessandro Baratta Ship in port of Napoli 1629
• Amsterdam Ship being constructed with visible gun-holes forward - 1697
• Ships in battle guns not visible but smoke indicates forward firing 1690 - 1710

This collection of images - from all over Europe - shows definite existence of guns mounted in the bow and stern, firing forwards and backwards. In general you can see most of them are rather low mounted, especially bow pieces which are rarely shown in the actual bow, but rather protruding from the hull. This is mainly due to the weight of the pieces which if mounted too high would highly destabilize the ship in bad weather and was mostly avoided.

As for the English in particular, I would just point out that mid 16th century Anthony roll ([First roll](https://commons.wikimedia.org/wiki/Category:Anthony_Roll_(first_roll)), [Second roll](https://commons.wikimedia.org/wiki/Category:Anthony_Roll_(second_roll)),Third roll almost all of the ships have stern mounted guns, and a lot of those have also bow mounted guns, especially the galleases of the second roll, and smaller ships of the third roll. In fact, even the carracks of the first role can be said they have bow guns as at least some of their cannons in the forecastle face forwards (which can be realized when you remember the castle is triangular in shape)

What does that then mean that "From 1799 Royal Navy frigates were universally supplied with two bow and two stern chasers". Not being the author I can't say much but is probably meant either in the context of regulations/standardization in the period, or in overall context that period in particular if for example chasers fell out of use, which I personally can not say anything about. What I can say is simply the concept of guns mounted forward and backwards itself existed since first equipping ships with artillery