English law prohibits (in certain fields - e.g. employment) both direct and indirect discrimination in relation to a "protected characteristic". Protected characteristics include "race", the definition of which includes colour, ethnicity, and national origins.
An example of direct discrimination would be if you required an employee to be of a particular ethnicity or not of a particular ethnicity - e.g. Welsh.
An example of indirect discrimination would be requiring employees to be at able to speak Welsh, which would mean that the percentage of English people who were eligible was considerably less than the percentage of Welsh people who were eligible. The thing about indirect discrimination is that is is allowed if it is a "proportionate means of achieving a legitimate aim" - so obviously requiring a teacher of the Welsh language to be able to speak it is fine but requiring a fork-lift truck driver in a warehouse in London to speak Welsh would probably not be.
So although language is not itself a protected characteristic, language discrimination can sometimes be indirect race (i.e. ethnicity) discrimination. The same could be true, in the right circumstances, for accent discrimination.
There must be very few, if any, circumstances in which requiring someone to have (or not to have) a particular accent could be "a proportionate means of achieving a legitimate aim" but the main difficulty in any claim would be the prior question of whether it could constitute indirect discrimination on grounds of ethnicity/national origins etc. in the first place I.E. would such a requirement affect members of one ethnic group more than another?
It might be difficult to argue that variations in accent in different English or Welsh regions correspond sufficiently with ethnic differences for accent discrimination to constitute indirect race (i.e. ethnic) discrimination. But I can see that indirect discrimination might be possible with regard to country differences. For example requiring employees not to have an Australian accent would, I think, be indirect discrimination on grounds of "race" (the definition of which includes national origins and ethnicity).