House advice

[spud131]

My wife and I reserved a new buld Cala house back in March and are part exchanging our current property with them. The move in date was moved from August to end of Nov due to the coronavirus.

We appointed our solicitors back in March and they have been utter shite providing no updates, not replying to phone calls or emails. This resulted in me emailing the partner of the firm with a complaint in July, I received a phone call from him within 30 mins apologising, blaming it on staff shortages due to the corona. He informed me the case would be passed to another of the solicitors to be progressed.
There was slight progress after this with the missives being completed at the start of August.
We heard nothing from them since the start of August and assumed everything was getting worked on in the background without issue.

At the start of last week we were contacted by Cala to make us aware of an issue with the title deeds for our current house (relating to the purchase back in 2013), our solicitors were apparently aware but didn't contact us. My wife was able to source paperwork from her old solicitor in 2013 and this was passed onto our current solicitors who had still not contacted us.
I then emailed them to ensure they had received this paperwork and for an update on the rest of the conveyancing work. I received a legal jargon filled reply explaining the current problem, but no information on how they planned to resolve this.
I replied asking how this would be resolved and for an update on the rest of the conveyancing work. I didn't receive any reply.
Three days later I emailed the partner again complaining, he provided a comprehensive reply explaining the problem with the deeds and the possible resolutions (which I was happy to receive) however he stated that the paralegal had discussed all this with me the day before and I had been sent several emails in the previous weeks (both of which were entirely untrue).
I replied (firmly but politely) challenging this and asking for proof of the emails I had been sent.
About 10 minutes later the partner emailed me stating that he was withdrawing their services as we 'appeared to be going down different paths' and that we would need to find new solicitors to complete the sale and that he would pass on all documentation to our new solicitors upon full payment of their fees (still awaiting their invoice to find out if they're trying to charge me the full amount quoted at the start).

I'm at abit of a loss as to where this leaves us now, we have a little over 4 weeks to find a new solicitor and for them to complete the sale/purchase. This is not sufficient time for them to complete all the work from scratch so will require the paperwork completed so far by our current solicitors.
Should I just pay the amount they quote so that we can get the relevant paperwork so the sale can be completed by the new solicitor for the move in date and just take it on the chin as a life lesson never to use them again?

Has anyone ever been in a similar situation that a solicitor has withdrawn their services and left them in the lurch?