Part exchange is a TOTAL waste of time unless you really badly "need" to buy something in a hurry and haven't got time to make a private sale. No shop will ever offer you what the guitar's worth because they have to be able to make a profit when they sell it on.
Say your guitar's worth about £800. The most a shop will give you in P/X is about £500, because when they sell the guitar for £800 they're going to lose a big chunk of that £300 profit as VAT. And another chunk of the remaining profit contributes to the costs of running the shop.
Whereas if you sell it yourself, if you're lucky you'll have £800 in your pocket. Even in the worst case you'll never end up with as little as you would by P/X'ing it.