I need a letter written to a former solicitor

This is for UK services only.

Last year I (my company, I'm sole director) purchased a property. The conveyancing was done via a local solicitors to me, the seller used the same company, but different solicitor.

I'm now selling the property, the UK Land Registry has agreed to expedite last years transfer of deeds (due to the ludicrous backlog), they wrote to my solicitors on 25th Feb asking for more information. My solicitor says they are waiting responses from their colleagues who acted as the buyers solicitor (they work in the same office, so I don't get why they are sat on it!) The new buyer is keen to complete ASAP, the Land Registry can't do anything until my former solicitor gets back to them.

I'm looking for someone to write a letter to them in legal terms to say get your arse into gear! I keep chasing and they just say the same line, they are waiting.