April can be a very windy month. The Western side can be almost as windy as Ireland - windier in fact sometimes in the Irish Sea as you get a venturi effect as Ireland and the UK pinch together in a triangle shape. So, yes, if you can take your kite gear without extra expense (or the forecast looks good) - go for it. The only thing to note is that in April the water can be cold (conversely it is warm in October/November), so take a thick wetsuit.
The UK has thousands of km of coastline so there are dozens of options. Certainly in Cornwall you could try Marazion, Gwithian, Watergate Bay or Daymer Bay, to name a few. Always Google a spot before you go out there as some spots are restricted (e.g. bird sanctuaries) or are zoned; and some only work at high tide or low tide depending.
Enjoy your travels and PM me if you need more.
Cape Town Kite Club
(and also Rhosneigr, UK)