Hello,
If your <lady> is here on a long student visa (6+ months) and there are more then 3 months left on the visa, she will be able to apply for a certifiate of approval (COA) and then get married.
Presumably, you are a British Citizen or Settled (ILR) person or an EEA national exercising a Treaty Right in the UK.
Work Permit employment. If your <lady> has graduated a UK educational establishment with a BA or higher degree, she may appy for WP not leaving the UK.
All the details can be found at
www.ind.homeoffice.gov.uk and
www.workingintheuk.gov.uk
Regards,
Anton