In principle, yes. There are very very few occupations which are now barred to bankrupts - I think they include solicitors and accountants and some people who work in financial services. If there is serious cause for doubt it might be best to check with the employer, but I think that in the vast majority of cases if the employer dismissed someone for becoming bankrupt it would amount to unfair dismissal.
There are some public offices that a bankrupt cannot hold (according to the clearstart.org website - it doesn't say what they are though. A different part of the site says you cannot be a Company Director, MP, Councillor, Estate Agent or Magistrate.)