London? Why go straight from Scotland to London and miss out what's inbetween, such as (ahem) Newcastle?
I've never been to London, but summer should be the best time to go. April won't be too cold, but English weather is hit-and-miss. Not too cold, not too hot, but it
could rain a lot. Then again, you could have seven scorching days of sun. All of August this year was nothing but rain and floods, ALL OVER the country, so you really can't tell.
Mick