He obviously has too much money!
Ok, well if u know what the fee is for the service I would send him this cheque straight away, along with a letter explaining that "despite many attempts to contact him you still have not got an invoice. however, payment for you services are enclosed. I will await you invoice for additional fees (such as land registry map) before submitting further payment".
That covers your end, and the ball is back in his court. If they dont get back to you it is of no fault of yours. I would recommend registered post and cross the cheque and keep a record of when the money leaves your account. Just in case it did come back to haunt you. However if you did the above you have certainly done enough on your part.
KS