There are isolation transformers and there are isolation transformers. Don't get confused between the two!

This isolation transformer is designed with the OP's application in mind (
http://uk.rs-online.com/web/p/safety-site-transformers/4368805/). It does NOT have a centre-tapped earth. I've just opened mine up to check. The output winding is completely floating, you can short the output live to earth, or the output neutral to earth with no problems, and you can even connect the secondary in series with the primary to get 480V if you really want. An RCD (or GFI if you prefer) on either end of the transformer will do nothing. This is good in some respects because if you touch the output live, you don't get a belt (in theory - I'll get to that in a moment). But if you're testing something that has an earth leakage fault, maybe an SMPS with a leaky cap in the EMI filter, you won't notice.
However, caveat emptor, you can still get a small shock if you touch the transformer secondary (live or neutral) and earth. Why? Interwinding capacitance (IWC). I measured 76V between output neutral and earth, and 38V between output live and earth with a fluke 87-V (10M input impedance?), and shorting to earth with the uA AC range I measured 36uA and 4uA respectively. Not a huge amount, but enough to feel it if you have wet hands. (Yes, I tried it). The IWC will vary from unit to unit, probably has something to do with temperature and will cause a higher leakage if you have harmonics on the mains. If you're trying to make sensitive measurements on an SMPS this IWC can give erroneous results. But it's much better than having the full mains across you. If you can find a transformer with an earthed electrostatic screen between primary and secondary, IWC is not an issue, but you still have leakage capacitance between secondary and earth.

This isolation transformer is different (
http://uk.rs-online.com/web/p/safety-site-transformers/2604272/). It takes 240V down to 110V for the 110V tools we have to use in the UK on building sites. It DOES have a centre tapped earth - the transformer secondary is wired as 55-0-55, with the 0 connected to mains earth. So between output 'live' and earth there's 55V and between output 'neutral' and earth there's another 55V.
Someone earlier mentioned that because there are two conductors carrying 55V you're twice as likely to get a shock. Maybe so, but it is FAR more likely that the shock will occur between one of the conductors and earth than between live and neutral. Perhaps you're standing in a muddy puddle and you cut through or nick the cable. Or maybe you're holding a Hilti drill (earthed) and touch a dodgy connection with the other hand. Remember these are for building sites. The shock is therefore limited to 55V no matter what conductor you touch, and that's a lot safer than the possibility of the full 110V and certainly a lot safer than the full 240V. Perhaps the
chance of getting a shock is increased, but at least if it happens there's no way it will kill you. Also, unlike the blue transformer, an RCD on the 110V side of the transformer will do something, but these site transformers tend not to be fitted with them.
So why bother connecting the centre tap to mains earth, if all you're interested in is reducing the likely shock voltage to 55V? The reason is that if you're drilling a hole in a wall on a building site and hit a buried cable at 240V (or even 415V), you're going to want that fault current to go through your drill bit, through the casing of the drill and down the 110V earth wire and through the transformer to the 240V incoming side, to earth. Not through the drill bit, through your hand, heart, other hand, aluminium step ladder, muddy puddle, earth. Or maybe you're sawing some floorboards.
Someone also mentioned the prospective fault current is reduced with these yellow transformers. This is true, because the voltage is lower, assuming a constant earth impedance. But it has the unfortunate side effect of not tripping the output fuse or MCB as quickly. But that's probably irrelevant.
Speaking of RCDs and death, years ago I was diagnosing a Marshall guitar amp with the customer standing over my shoulder and breathing down my neck. It has an earthed folded metal chassis and the IEC inlet (with uninsulated spade terminals on the inside) on one side. I turned round to the customer to give him the lowdown on what was wrong with his amp. My left hand was in contact with the amp chassis, and as I turned my right hand touched the live spade on the back of the IEC. In other words, I had the full 255V mains (our mains is high at night) across my heart. FUUUUUCK! I screamed loudly as I flew back a few feet. The 30mA RCD tripped and the workshop was plunged into darkness. I think the customer was more shaken up than I was, which is saying something. Had I of used the blue isolation transformer, I would have been absolutely fine. Accidents happen in this business, no matter how experienced or careful you are. (Send your repairs to That Crazy Norfolk Bloke, Unit 3......)