Disclaimer: This post does not constitute legal advice in any sense of formal service and should not be relied upon in any serious or legal matter. Proper care should be taken with such a matter and if you wish to proceed, with peace of mind, you should seek professional legal advice.
This is a very good question, one that is certainly not immediately obvious, even though I have studied copyright law! I went out and did some additional research to come to the following conclusions.
It is in fact illegal to use a trademarked logo in any way shape or form. All you're doing is use popularity and fame of the Intellectual Property for your own personal gain and that's how it will be seen in a court. There are no real guidelines as to how much of the logo you need to change for it to be considered safe in any way. Some people might talk about fair usage, but they don't apply on the previously mentioned issue that you're using the brand name of another company to make money.
Whether or not you get prosecuted is another matter entirely. The chances, apparently, would appear to be relatively low. The trademark holder or copyright owner has the right to pursue you in any case of copyright infringement but it will be a civil case, which means that you will have to pay any and all of the fees involved - unless you win. It will also be an incredibly stressful situation for you, as it is highly possible that the legal fees alone will far exceed any financial gain made with the t-shirts, and that's not including damages you will have to pay if you lose.
It would appear that such cases are rare and in fact there are many, many outlets doing this on a daily basis. I imagine the risks would be relatively low and that in comparison to other companies doing the same thing, it is unlikely that, for example, You tube would go after you because you're simply too small for them to care about - unless they are looking to make an example. It's more likely that they will go after larger retailers first, like Zazzle and others. In your case though, as an individual, it would be more likely that you receive a cease and desist order which will require you to stop, otherwise face the impending doom of legal action from a multinational corporation!
I believe that this is a fairly recent issue in terms of the law, and as such current UK law is not really set up to deal with this situation very well. So I imagine, if it's not already under consideration, that they will make amendments to the law to include such scenarios in the near future.
Chances are you can do it and are unlikely to get caught, but I read some good advice which I'll pass on, which is to simply set aside some money for legal expenses, just in case. This will also set your mind at ease to some degree, knowing that you are at least a little bit prepared if it does ever happen.