According to the TfL website, it'll cost me £3.20 to get from Surbiton
[National Rail] to Brixton [London Underground] ...

However, won't I be exiting at Vauxhall National Rail before having to
get back on again at Vauxhall Underground?

I checked by putting in Stockwell, however this made no difference.
(Thinking it may want to route me via CJ and Victoria to Brixton).

Thanks