Under the Equality Act 2010 in the UK, it is illegal to discriminate against someone because of their philosophical belief, including veganism, if that belief is considered a "protected characteristic." However, simply not offering vegan options on a menu would not necessarily be considered direct discrimination on the basis of philosophical belief.
Indirect discrimination occurs when a provision, criterion, or practice (PCP) is applied equally to everyone but disproportionately affects a particular group of people. For example, if a restaurant only offered a limited selection of dishes, none of which were suitable for vegans, that could be considered indirect discrimination because it would disproportionately affect vegans.
It would be important to prove that the restaurant does not cater for vegans on the menu, and that it put them at a substantial disadvantage, and that there are no legitimate reasons for the restaurant to not offering vegan options.
It would be up to the courts to decide whether a lack of vegan options on a menu constitutes indirect discrimination on the basis of philosophical belief, but it's possible that this could be the case, especially if the restaurant could reasonably accommodate vegans by offering a sufficient selection of vegan options.
However, If a restaurant, on the other hand, was catering for a diverse group and it is not commercially viable for them to cater for every dietary requirement, it would not be considered as indirect discrimination.
It is worth noting that, Many independent and chain restaurants now offer vegan options to cater for a diverse group of customers and to address ethical concerns around animal welfare.