I will be flying in and out of London for a 10 day vacation. Is it possible to effectively visit London, Wales, Scotland, and Paris? Any suggestions for an itinerary?

Not effectively, no. If you've never been to London or Paris before, I'd personally do five days in London, then train to Paris, and five days there. But, you may have a special interest in Wales or Scotland, and if so, maybe you should do four or five days in London and then the other five or six in whatever part of Wales or Scotland interests you (but probably not both, that would be rushed).

Agreed - for 10 days pick your top 2 locations, otherwise you will spend more time in transit then you will actually enjoying the locations.

If you have already booked your flights I would fly from London directly to your next location on arrival (say Edinburgh or Paris) and then spend the last 5 days in London to avoid the hassle of having to get back to London right before a flight.

If you havent booked your flights book an open jaw flight into one city and out of the other.

No - it's not.

In 10 days you can do a quick look at London and Paris.

Or London and a little bit of Scotland OR Wales.

The trip you want to take would need 4 weeks to see major sights.

For 10 days you simply don't have enough time. That would be like visiting NYC, DC, Boston, & Toronto for said time period. Pick another location to pair with London. Paris is the perfect companion for such a trip... Or Edinburgh. Depends on your tastes

Well actually, the OP picked 2 cities and 2 countries.

So more like visiting NYC and DC and then going to tour CA and perhaps Texas.

Welcome to Fodors drdlowry. The places you want to visit could fill months let alone 10 days. What specific sites if any are you wanting to see?

You could easily spend ten days in either London OR Paris with a couple of day trips out of either city. Or you could spend ten days in Scotland and see a VERY tiny portion of that amazing country.

So - what research have you done, why did you pick those p,aces specifically, - give us more to work with and we can help you figure out where you want to go . . . But London, Paris, Scotland, and Wales - you'd need 5 or 6 weeks to even scratch the surface.