I agree with habdab that it is a true bug (Hemiptera), and most probably a shield bug (Pentatomidae)
However, hudl, when making comparisons with images on the internet, bear in mind that yours is not an adult. It looks to be a final instar (last nymph stage before adult). The appearance of true bugs changes considerably as they develop.
Nezara viridula (southern green shieldbug) is not far off, but certainly not identical - see
Notice how individuals, even of the same instar of the same species, can look very different - look at the last three photos on that page - they are all final instar nymphs. Yours may yet prove to be of this species.
There are plenty of other bugs listed on that (excellent) site, including these drawings
Maybe it is not British?
Do you live in Britain?
If you can keep it alive, you may witness its transformation into an adult, which would be nice, and which would help identification considerably. Be prepared for it to be completely green!
BTW, if you find yourself getting interested in true bugs, have a read of this introduction by the NHM
Mark Hardman, Yes the bug is still alive, it is in a jamjar with a leaf from some brocolli. It came with some blackberries from Tesco which were from Mexico. Maybe it has come from there? Yes I do live in Britain.
Will see what happens to it.
Keeping the bug:
If possible, keep the foliage fresh - better to have a sprig in water, and if you can find any brambles with new leaves, that would be worth trying. Many insects are fussy about their food!
Watch it and try to notice it eating (sucking). If it does that, it probably likes what's on the menu
Yes, it could have come from there on your blackberries. These little creatures can get around on crops. For instance, there are shield bugs in the USA that came from Africa. If it did come from Mexico, it could still be Nezara viridula, as that is recorded from Central America (Honduras in this case - http://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1030&context=insectamundi).
I am finding it difficult to discover good pictorial references to Pentatomidae of Mexico, so anybody with access to relevant printed reference works, please contribute!
The best one for North America is http://bugguide.net/node/view/182/bgimage. But I have looked through 5,700 images of bugs without finding a match for yours
Here are some more Nezara viridula nymphs - http://bugguide.net/node/view/333579/bgimage.
Thyanta is another possible genus.
Printed reference of potential relevance:
Stink Bugs of Economic Importance in America North of Mexico
By McPherson, E. and Robert McPherson
CRC Press, 2000
(yes, that's 'North of Mexico', but they get around)
May I suggest that if you have a sprig of foliage in water, then cover the water with a layer of cotton wool to prevent the bug from accidently drowning. Not too sure how suicidal bugs are but I know Reptiles can drown easily in captivity.
Thanks for that, will put some greenery in wrapped in damp kitchen roll to help keep in fresh. What I'm going to do with this bug if it doesn't die I do not know, I certainly can't let it out as it may not be native.
If it survives, we stand a better chance of identifying it, and then we can decide (perhaps) if the authorities should be notified.
Precautions against bug drowing would do no harm, but in this sort of case -where there is a plant stem serving as a route out of the water- I think the risk is relatively small, especially if the stem is kept in touch with the inside of the vessel.