Your best bet is to get them a set of Olds Ambassadors. Used. Probably the least expensive, highest quality "student" horn out there. The little ones could use cornets instead of trumpets. Cornet is a bit shorter, the "long bell" design more typical of American cornets can sound very trumpet-like with the right mouthpiece on them. Louis Armstrong started out on cornet.
Other advantages...you could fairly easily get your money back out of used horns if you were ever to find yourself in the position to have to sell them "from lack of use". They'll be a LOT less expensive than buying new.
A cornet for the little 'uns places the sound a bit closer to their face so they can hear themselves easier, the horn is shorter so the valves are easier to reach for "little hands and little arms", and a cornet is just ... "funky" to own and play.
Other brands that are good buys from the used market would be the Yamaha student line trumpets and cornets (you'll probably have a better chance of finding them "over there" than the Olds line). Any Kanstul-made horn (American) is considered to be very high quality for the price...great value there. They used to contract build for Boosey & Hawkes for the N. American market (but not the Euro market...B & H had those horns made elsewhere..not sure where).
I understand there are a couple of good brass shops in London. Another guy who might be really happy to get you a lead on some horns is Roddy...he lives in Wales (I think) and his website is
http://www.r-o-d-d-y-t-r-u-m-p-e-t.cc/home.html. Send him an email and explain your situation. He posts in this TM website from time to time but may be busy and not having time to read these right now.
Edit: Oh...those "new" trumpets for 150 pound or less? Stay FAR away from them. They are junk that is mass produced somewhere in Asia. Any resemblance between them and a musical instrument is purely coincidental and limited to appearance (from a distance) only. If you want your family to give up music get them a set of those...otherwise buy a recognized "name brand".