To resolve this without wasting any more money on solicitors, you need to write a formal letter of complaint to the building society (keeping a copy), setting out the details of your complaint, pointing out their negligence resulting in you not receiving your rightful share of your late father’s estate. You should point out that you have made reasonable attempts to contact your sister in order to resolve the matter, but without success.
The complaint letter should set out the redress you are seeking (sum of money), including how you arrived at that figure. Besides your share of your late father’s estate, you could reasonably include the funeral costs you have paid and any other incidentals in relation to dealing with the estate. Unfortunately you are unlikely to be able to claim monies you have paid to your solicitor (unless the matter is ultimately placed before a court, where costs would be awarded).
Within the letter you should specify a time period within which you expect the matter to be resolved to your satisfaction (a reasonable time period might be 15 working days, possibly longer if the estate value runs into millions of pounds); otherwise you will be making a complaint to the financial ombudsman re their negligence resulting in financial loss to you.
You should send the letter to the manager of the branch you have been dealing with, and to their UK registered headquarters (I would suggest you address it to their CEO, do a bit of on-line research and find their name). For each letter, request proof of posting or some form of delivery proof.
If they respond to your letter, it is likely that they will try to fob you off claiming you should sue your sister for the loss; you could reply pointing out that their negligence resulted in this situation (personally I would not reply to such a letter, or I might reply pointing out that the matter was not resolved to my satisfaction and restate the deadline at which time the matter will be placed before the financial ombudsman).