From what you have said, you have only reserved the property. Therefore there is nothing to stop you changing your mind about using their solicitor and stating you want to find your own independent one!
If they refuse, at the most you will lose is a couple hundred pounds. If they refuse then this probably tells you all you need to know. You have not paid a deposit at this stage therefore not a massive issue.
The problem with stating what should be in the contract is in fact what a good solicitor should be advising you on!
As already stated completion date for Nov/Dec is problematic to say the least, even when not under the pressure of end of year figures getting them to provide a snag free house I would say is almost impossible.
Just remember as a buyer of an off plan house, they are keen to get as many houses sold in advance as possible. Please tell me you pushed hard for a decent discount? Remember with Brexit, a lot of people are not as willing to make big purchases. There's a chance houses prices will decline especially in the short term and remember you will already be paying a premium for a new build.
My advice, it might be worth waiting a few months to see how the economic shock takes hold, the last thing you want is to a buy an already over-priced house to see your equity diminish further through a market slump.
If you are adamant, then please read this website thoroughly and then read it again. It might sound a bit hypercritical me saying don't use their solicitor when I did, but then again my house builder doesn't have the sheer volume of unhappy people yours does!
Good luck, be smart