Hi Wooden-heart, and welcome to the forum!
To add to Jimi's list of good names, the ones that seem to be sought after by the carving experts are Addis and Herring, with Henry Taylor (Acorn brand) almost as well regarded. Of the more modern toolmakers, Ashley Isles are very good. By the way, there were quite a lot of Sorbys - I Sorby, I&H Sorby; and Robert Sorby are still in business. Tyzack is another good one. There were also lots of smaller firms (W. Butcher, Colquoun and Cadman, for example), so don't worry too much if you don't recognise the name at first - if it's got 'Cast Steel' stamped on it, it will probably be good.
Sharpening is one of those areas in which you could spend hundreds on specialist kit, but you don't need to. There are three stages - grinding, honing and polishing.
For grinding, the cheapest way to solve the problem is to find a secondhand hand-crank grinder. They crop up on Ebay quite regularly, and sell for £20 to £80 including postage, with 'restored' and 'original' examples fetching the high prices. You don't need a fancy one, as long as it's all there it'll work. You may drop on one at a car-boot sale or in a junk-shop even cheaper.
Honing is the 'oilstone' stage, for which there is a bewildering array of possibilities these days - oilstones, waterstones, diamond stones, or (just as effective) wet-and-dry papers of different grades stuck to pieces of wood. You can thus make 'stones' to the shape you need, and if you buy a selection of grades from about 80 grit through to 2000 grit, you can work from grinding through to fairly fine polishing.
The last stage, polishing, refines the edge. There are several ways - very fine wet-and-dry as above, or stropping using a piece of leather stuck to a piece of wood, and dressed with a very fine abrasive. Worn-out leather belts make good sources of strop-leather. The fine abrasive can be jeweller's rouge, fine diamond paste (available from Arc Euro Trade at less than £5 a tube, and very effective by all accounts), chromium oxide paste, or even toothpate may be worth a try - that's a fine abrasive.
There are quite a lot of short videos on Youtube giving guidance on various methods of sharpening and carving techniques. Some of them advocate expensive power sharpeners, which make sense if you're a professional trying to make a living from carving, but are not at all necessary for the home workshop. Nonetheless, there's good tips to be picked up on Youtube.
Look out for a couple of mallets as well. Carvers traditionally used the round ones, and it's useful to have a couple of different weights - a big 'un for heavy waste removal in the early stages, and a small one (sometimes a small brass one) for finer work.
However you decide to go about it - have fun!