If they didn't point out that a chunk of your garden wasn't actually going to be your garden, then that's really deceitful of them and I would be asking them to take a bigger chunk off - how much percentagewise of the garden is it? And if part of the access and side garden is involved, that's even more...
Have another look at the details - did they include or mention or show on pictures any of the 'not legally yours' bit of the garden? If so - (and even if not, if they showed you around the house and didn't mention the issue) then... (assuming they are no overrun with offers!)
If you thought that the garden was small anyway,. then I would go back to them, point out that this is a big deal as the garden was already too small for you really, you want to pull out, they have caused you to waste lots on legal fees, all because they didn't advertise it correctly, which means you believe that they have priced it wrongly and that actually the right price is [a big chunk lower. say £25k].
Say that you would be prepared to pay £11.3K lower if they sort it out beforehand - hopefully the difference between £25k and £11.3k would more than cover the land so that they would be quids in if they sorted the land out - if not tweak the figures so that you want to take off more than the land is worth to encourage them to sort it out to save you the hassle and to ensure it really gets done.
Regarding choosing £11.3K rather than £10K or £11K - if you choose a round number people just assume that you have randomly chosen a round number that works for you. If you suggest a number that is not a nice neat convenient number, then people assume that you have a good reason for choosing it... (which you do - to make them think you know the proper number and haven't picked it randomly 
) and don't try to bargain you down half as much. Doesn't always work but works a heck of a lot more than it should do! Plus it gives you some room to negotiate and still cover the £7K difference.
And yes - agree with others - that housebuying is full of hurdles and if this is enough to be a sign not to buy together to him then it's definitely a sign all right - just not the one he is assuming.
If you do buy the house and he moves in, make sure that you get it set up legally so you can charge him to lodge with you and pay his share of the bills but that he doesn't have any claim on the mortgage or property if/when he goes. So, make sure he always pays you rent, and that he never calls it his mortgage payment - doesn't matter if that's what you spend it on or not. If he tries to pay you a cheque that says in the reference it's a mortgage payment for example, always send a paper trail (or email or text but make sure you keep it!) to say, no this is just your rent payment, and the bills you owe this month are £xxx.
There was someone on MN quite recently who was caught out by a partner who wasn't on her mortgage but who, when he eventually started to pay her rent, put the cheque in her account referenced as mortgage payment to try to use it as proof that he had paid the mortgage and deserved a share of the property, she was considering giving him some just to get rid of him because of the grief it was causing her 
so definitely worth thinking about!