I have worked in estate management for a long time. Firstly, your daughter CAN sell her property, the details just need to be changed. The land registry is not 'saying' her flat is a two bed 1st floor flat, they are 'saying' that is what is in their records, which can be changed.
The original solicitors should be responsible, but proving it was their fault and not an administrative fault at the LR could be difficult. The link below gives a lot of information on rectification of a LR mistake. You daughter needs to Instruct her solicitor to start rectification process and perhaps a stern letter from them to the original solicitors may result in them paying towards the costs of rectifying what you feel is their mistake.
https://www.gov.uk/government/publications/rectification-and-indemnity/practice-guide-39-rectification-and-indemnity