Hello, I'm Keith and happy to help you with your question. I will try to summarise this 'yes and no' situation for you.
No, if the club is registered then only the club is liable for any outstanding VAT arrears. But soft, there is more here to consider. Have a look at Jameson and Smith's guidance on this matter here:
Although it refers to companies you will see that if activities have been allowed to become seriously out of hand some blame might be attributed to managers. Presumably the club is an unincorporated association. In that case there is always the danger that all members could be held jointly and severally liable for the club's debts. Jointly and severally means that if some members cannot pay the organisation's debts it falls to the rest and the others must chip in, It is precisely as a defence against this situation that many clubs and societies incorporate to protect their members. My own club, founded in 1910, certainly did as far back as the 30s!
I do hope I have thrown some light on this matter for you.