Write the solicitor a letter telling him that you are unhappy and that you want your property registered as soon as possible. Give him a deadline to lodge the registration appliction in the land registry and ask him to send you a copy of the form 17 evidencing lodgment. Some of the documents relating to the transaction may need to be resigned by the vendor and yourselves because of the lapse of time. So give him a couple of weeks to take care of this. Threaten to report him to the law society if you don't get the form 17 within the relevant time period. You could also tell him that you are considering selling the property which may move him along
If his fees and outlays were paid at the time then any additional costs arising as a result of his delay are his problem. Land registry fees have increased dramatically in the last few years and I presume he is looking for these. But the increase in fees was well flagged and he should have got your documents in before the increase. He is under an obligation to your mortgage lender, as well as yourselves to register the title and their mortgage.
Retaining another solicitor may be a good idea if you don't get a satisfactory response, one working near him may be best as it could embarass him into movement, also a local solicitor will have a good idea of whether this is his typical behavior or a one off genuine mistake.