And please don't come back to the thread and drip feed that it is a listed building
Oh dear god no, definitely don't do that!
Thanks @Aridane 
Don't buy the house. Walk away. Even if you have exchanged contracts it will be cheaper to accept the contractual penalties for pulling out than it will be to go ahead with buying a money pit like this.
^ this is not good advice. If you have exchanged contracts, which I assume you haven't given that the building regs issue was still being sorted, you need to be absolutely clear on what the potential contractual penalties might be before withdrawing.
After 4 years the LA can not enforce building regs non-compliance anyway. Assuming the work was done more than 4 years ago you just need to be satisfied that it’s sound.
That's not actually the case. Planning is 4 years if no planning permission, 10 years if breach of conditions and no concealment. Building Regs is usually 12 months but there is actually no limit on the enforcement period if the work is unsafe and causes an issue.
In terms of the building regs for the extension, given the age I wouldn't worry. A lot of Local Authority building regs records don't go back before the early 1990s. I would however get a structural engineer to confirm that the work and structure is safe.
@Neet90 if the work to the beam was done in the last 12 months they might not have been able to get indemnity insurance anyway, depends on the insurer.
@kirinm What is your issue with the conveyancing solicitors on this thread? On the whole they have made the OP aware of the various options that might now be available to her. FWIW I would be wanting a regularisation certificate for this work.
If someone was content to accept indemnity insurance I would always strongly recommend that they also get a structural engineer to check the work is actually safe.