Both BA and VS require purchase of specific Economy fare classes to upgrade to Premium Economy.
BA requires 25,000 miles (to North America) and purchase of a Y, B or H fare*. You can create a hypothetical BA booking to test pricing by logging into your Executive Club account on ba.com and choosing: Book and upgrade with Miles. You can see BA's upgrade rules here...
https://www.britishairways.com/trave..._us?sl=upgrade
VS requires 20,000 miles and purchase of Y, B, L or (on some routes) M fare. The VS upgrade rules and a tool which would allow you to create a hypothetical booking to see typical costs of upgradeable fares are here...
http://www.virgin-atlantic.com/en/gb...ghts/index.jsp
*My Executive Club account is in the USA program. It is possible that the rules for UK based members are different.