Amanda, the tape you want is much longer than anything meant for brewing or aquariums. It's called 'trace heating tape'. The best place to find it would be a builder's merchant that does bits for plumbing.
I've never seen anything like this which you could run from a leisure battery - the power required is just too great. Sorry, but it's mains or nothing.
The sites I've looked at make the point that, even when trace heating is used, you still need the usual foam insulation on the pipes as well - you know the stuff that looks like a grey foam plastic sleeve - otherwise too much heat is lost.
Another site I looked at said that lagging pipes with the grey foam will not prevent them from freezing, though it will slow the process. But, it said, if a pipe is outside, and the temperature stays below freezing for more than a few hours, the pipe will still slowly freeze up regardless.
There are firms who supply complete frost protection kits, but they're not cheap - £100 for a 10m run of metal pipe.
Trouble with the kits is that most of the cost is for the thermostat.
If you're happy to save £60 - £90 by switching it on and off yourself, this company (see link below) sell just the tape. The one you'd need would be the VC type (frost protection), which is either £5 or £6 / metre, depending on the power output. With that, all you need to do is to hook it up to the mains.
www.express-industrial-exports.co.uk/html/trace.html#priceIf you can use a mains powered tape, to protect the tap, just run the tape up the pipe and around the bottom of the tap, and cover the tap with something like an old 4 pint milk container, with the bottom cut off, and filled loosely with straw. When you need to use the tap, lift off the milk container and use the tap as normal. As long as the tap is covered like this after use, enough warmth will creep up from the tape, through the water inside the pipe and tap, to stop it freezing.
VERY IMPORTANT POINT!!I would very strongly recommend that if you have any 240V equipment working outdoors, or where it might get splashed, trodden on, etc, that you use an RCD plug on the cable, where it's plugged in to the 13A socket in the house, barn, etc. You can get these from garden centres (they use them on electric lawnmowers), and Argos do one for £8 which is like an adaptor which plugs into the mains socket, then you plug the outdoor lead into it (page 1159 in their catalogue). They should
always be fitted where the cable plugs into the wall. If you're using anything which plugs into an extension lead, fit the RCD where the extension lead plugs into the wall,
NOT between the equipment and the extension lead.
RCDs are designed so that, if the cable is damaged, and the most minute leakage current is detected, they cut the power faster than your muscles can respond to the shock.
Hope this helps, but if you need any more info, let me know. I'd
much rather that you, or anyone else, sent me reams of PMs than that you take a chance with electricity!
Best regards,
Jack