Lambda reading is high, which means lean mixture or excess oxygen in the exhaust gases.
Could be an air leak. This will introduce extra air into the engine above that which is metered, meaning a lean mixture. Certainly, if you suspect a problem around the EGR, check it and resolve it. Look for air leaks into the breather pipes, multiram vacuum system, brake servo hose (prone to chafing and getting leaky).
Normally, however, this would be adjusted out by the closed-loop operation of the Lambda sensors. They will correct the fuelling or, if it's too far out, raise a trouble code.
It's possible that you've got extra air entering the exhaust through a leak somewhere, I suppose. I believe an MOT emissions tester should compensate for that when calculating the Lambda value. :-/
It's also possible that the engine is not in closed-loop mode for some reason. If the coolant temperature is low (or being reported low to the ECU!) this might be the case, for example, hence the recommendation to check it's warming up fully. Still, could be that the engine ECU is not seeing the correct coolant temperature so is still running open-loop.
I guess the car is off the road? Otherwise, a check with a Tech 2 would certainly shed some light on it. Might be pushing it a little, legally, to bring it over for a "pre-booked" MOT near Alton?

Kevin