The first answer is correct, a taxi would be a waste of time and money.

The underground isn’t a bad idea, although it might involve a bit of walking (the changes are awkward from Euston to Wembley; I’d probably get the Metropolitan line west from Euston Square to Wembley Park instead, which would be a single journey).

However I think it would be even easier to simply catch an overground train from Euston station to Wembley station. This would cost about £4, then a taxi from Wembley station to your destination would be more like £10.

EDIT: I’ve just thought of another advantage to taking a train from Euston to Wembley. Have you bought a train ticket to London yet? If you haven’t then simply request a ticket to Wembley via Euston, rather than just to Euston. Why? because chances are the price will be exactly the same.

By the way, don’t think I’m assuming you’re some kind of cheapskate here! The fact is that London is a pretty expensive place, so having an extra 20 or 30 quid in your pocket would be no bad thing, whatever your budget.

If yoy’re coming into London Euston by London Midland or Virgin Train,
simply catch one that makes its last stop before London Euston at Watford Junction, and change there for a local train to Wembley Central. or catch the local service from Euston to Wembley Central.