Yes, you can rent a scanner, but the easier thing to do is just call the reception centre where your animal will be taken.
Avid chips (if I am not mistaken) are the mainstream in the UK, so you shouldn't have to worry anyway.
My dog had HomeAgain, and I called the reception centre (they are really nice in Manchester) to ask. No problems at all.
Like you, I worried about this for no reason because you can just call and ask! If you know where your dog will be going (London, Manchester, etc..) YOu can look online (do a search..manchester animal reception centre) and find the contact details.