I'm thinking of getting an adroid tablet from the US and ship it over here to the UK. Will it work completly and as a UK based tablet? I don't need 3G.
This may depend somewhat on the device, so I would try to narrow down which one in particular you want then try to figure out what other people are saying about it. Having said that, I know lots of people on XDA are using US Verizon Xooms in Europe without any problems (minus 3G, of course, which you said isn't a problem). There's a thread about this here. Some have also noted that you can flash European firmware onto the VZW Xoom without any problems, but I'm not sure what the caveats are and I don't know if that would work on other devices.
It depends on your tablet. If your tablet has included CDMA technology that is not available in UK then it can't possible to use that tablet. Tablet with Wi-Fi technologies will definitely helps to work in another country but it's also depends on tablet network connection features. As per my view, you should include little information about your tablet.
Tablets that use CDMA network technologies will be restricted to wifi internet only (there's no CDMA cell coverage at all in the UK). If you can get a tablet that uses T-Mobile's 3G frequencies, you can SIM-unlock it and use 3G with an operator in the UK. AT&T frequencies are not common in Europe, you'll get EDGE only.
Wifi will work, but Europe/UK uses a different channel/frequency standard and you won't be able to use channels 12 or 13 (at a minimum; it could be only a few channels work if the spaces between the channels are different; I haven't stared at the standards recently).
If you can tell the device to use the EU ranges, you'll be fine - but I'm not sure how to do it - If Android uses the Linux kernel's regulatory compliance daemon, that's fairly easy to change because the commands should be similar to a Linux desktop and there's quite a few tutorials out there.
That assumes Android uses that part of the Linux wifi stack, and it also assumes that the wifi driver in the tablet actually uses the Linux stack to drive compliance. This is not very likely. :(