Can I still claim constructive dismissal when off on long term sick?
You need to be careful here.
Recent case law has come down against an employee who claimed she was too ill to resign while on long-term sick. The Employment Appeals Tribunal held that she had in fact affirmed her contract by both her delay in resigning and her conduct. The ET held that although the delay in itself did not affirm the contract, affirmation was implied by her conduct- in particular accessing and using her work email, discussing her continued employment, and continuing to receive sick pay.
Each case will be determined on its own facts, but if you have constructive dismissal claim to make, you don’t want to be making positive noises at the same time that you are happy to stay employed.