There's basically encapsulators and converters.
Besides the Halfords, Kurust, etc products try Bilt hamner - Deox gel (converter) is good but takes time and severe rust can take 4+ applications to get back to bare metal.http://www.bilthamber.com/
You will be left with clean steel but if the rust was sever it will be scarred from the rust - so it won't be flat, you then have the fun of filling with hi-build primers etc if you want to touch in the paint.
We've just done my lad's Rockhopper in the same way and nearly all back to bear metal now - as it is metallic green bordering on the turquoise we may just end up using acrylic lacquer to coat the scratches and leave it scarred but stable.
Oh and yes try a bit 1st but Deox doesn't generally damage surrounding paint.
cheers & good luck
Like a fish ever needed a bicycle anyway...MTB: '89 MF Alu Team Pro,'88 Muddy Fox Courier,, '92 Orange Elite (now 17"!), '04 Kona Fire Mountain (now Son's), '96 Muddy Fox Ranger home-build (son's), Specialized RockHopper '92 (Ad's retro-build) ,'02 Kona Scrap Special Edition OB (3rd Son's), 1989 Orange Clockwork (Gone!?)
ROAD 2013 Orange CarbO ,2012 Basso Devil (3rd son's), Colnago CLX3.0 Di2 self-build