Try not to worry about it - if the university is made aware then I'm sure they'll be sympathetic.
When you're actually writing the dissertation, make it your main concern to just spew out all your ideas onto the page. Don't worry about spelling and grammar at all in your first draft.
Then go back over it, paragraph by paragraph, using the spellcheck facility - it'll give you several options as to what you may have meant. If you're not sure which one to pick, check each option they give you using a dictionary. This will be time-consuming but I'm sure it can be done.
The more difficult bit will be identifying phonemes (dear vs deer, there vs their etc) which most spellchecking facilities won't pick up. Again, go through all of them with a dictionary.
Finally, everyone writing a dissertation is allocated a supervisor - believe me, you're not expected to do it with no support at all! Try and get them to go over it (purely from a spelling/grammar point of view) and see if they can point out any mistakes that you haven't seen.
As I've said, this will be time-consuming, but if you just take it step by step then there's no need to worry.