I want to get a portable VOIP service that is UK based and which uses a UK number. Are there any such Vonage, lingo, Magicjack services like this?

Voipbuster and the other Betamax companies used to give UK incoming numbers for free (I got one). They then stopped giving them, and subsequently they started issuing them for the princely sum of two Euros.
Expect rock-bottom (or totally free) prices, good-to-great call quality and reliable operation, but virtually no customer service (though they do have a user forum). Nevertheless, it's well worth it IMHO, because it's cheap and it just works. Plus you can even use it with a slow connection, as there's the "phone to phone" option that allows you to connect any two phone numbers.

I should have added that I am looking for one that allows calls to UK cell phones for free as well....

You aren't going to find that! Calls to UK mobiles are quite expensive...
Outside of same-network calls (e.g. from Vodafone UK to Vodafone UK), I am not aware of any "unlimited" plan sold by any (mobile, landline or VOIP) telecoms provider.

In all of Europe, unlike in the states. That's why in the US, companies like Vonage can offer free calls to Europe, EXCEPT mobiles.

I use future-nine which is about the cheapest I've found for European mobiles. UK mobiles cost me fifteen cents a minute.

Incoming calls to mobiles in europe (and just about every other GSM country) is free, because the caller pays for it. It's called CPP (Calling Party Pays). That's why you will not see anyone offering free calls to mobiles in these countries.

I think OP's talking about making free outbound calls to UK cells.

He probably hasn't thought about whether the recipient's paying or not.

As for free incoming calls, I haven't been to too many countries (yet), so not sure if US is the only country that charges both the caller and recipient using cell phones (meaning answering your cell is using your "paid free" minutes as well). Certain Asia countries, such as Japan and Taiwan, incoming calls to cell are free. That's why some budget-conscious cellphone users ask you to call them instead of them calling you.

Voipbuster is one of the "low-budget" European VoIPs. There are quite some offsprings from the same mother "company" (Voipstunt, for example). I tried their earlier product from the States when unlimited outbound calls were offered. Not sure if they had evolved like Skype (Skypeout, Skype Mobile) though.

In response to #8's question about other countries that charge for inbound calls:

The US is not alone on charging for inbound cellular calls, but I'm pretty sure we are the minority. Off my head I know that Canada, Russia, China, India, Bahamas, Bermuda, and Hong Kong charge. Mexico is free incoming in only your home region only.

While not free, many of the VoIP services like Voipbuster, etc. do offer rates to mobiles that can be a lot cheaper than calling from a traditional landline - they are usually eliminating the international dialling portion, where the phone companies normally make some further margin.

For example, calling a UK mobile from voipbuster is EUR 0.18 / minute. Calling this number from a US landline could easily be more than $1 / minute, so there are some big savings to be had.

They've always been light years ahead of Skype. VoipbusterPro is the best example of them all; you pay EUR5 annual subscription, and you can call landlines in almost 50 countries for 3.9 Eurocents per hour! On top of which you get to send SMS for free to a dozen countries (incl. UK and US).

I believe the U.S. FCC has specifically barred CPP in the U.S.

We actually have allowed caller-pays and experimented with it with area code 500 calls. It was a miserable failure.