...womblin' free (sorry)

Say I need to catch a train from Euston station at 1324 on a weekday. I'm arriving in Euston by tube. How long should it take a regular human being without baggage to get from the underground station to the overground station and catch that train? Is it anything like Japanese underground/overground combination stations where it could take up to 15mins to get between them?

(Sorry, Japan is my only frame of reference with this)