I'm afraid I agree with your solicitor. The wording refers to an "assignment" of the lease being possible, but that means a sale of the leasehold interest, not a subletting. Accordingly, the lease does prohibit subletting.
Ok thanks. Do you think I could still start a negligent claim against the solicitor for not spotting this on day one, after all they had a copy of the lease and also knew it was a buy to let mortgage. I will never understand why it took them nearly 4 months to realize there was a problem against subletting?
Yes, maybe. If they were fully aware that the buyer was buying to sublet, they really ought to have checked the lease to see if consents would be required, if nothing else this woukd have helped avoid a delay. I think you could complain, but I am not sure you will get the £7,500 back.