You wouldn't be allowed to shoot steel BBs on the NEFTA course, due to the danger of rebounds off steel targets. I believe lead BBs would be allowed, but in any case a BB gun would not be accurate enough. You want a pistol with a rifled barrel that shoots lead pellets. Most people choose a precharged or a single stroke pneumatic. You won't get a precharged in your budget, but the aforementioned HW40 is a good choice. Low-ish power but very accurate and an excellent trigger.
Also the Webley Alecto is outside your budget but available for around £150 second hand. This has the facility to put 1, 2 or 3 pumps for better power. This extra power can help on the longer range targets, which can be out to 25 yards.
Although you can shoot it with open sights, it is more difficult, so you will find most people shoot with an optical sight of some sort (scope or red dot). I'd say the ideal starter setup is a Webley Alecto with one of the cheaper panoramic style red dot sights (around £30 on ebay or from JSR).
A very budget friendly option is the Crosman 1377. Very accurate, variable power, but a little agricultural and has a heavy trigger. No facility for mounting optics out of the box, however you could probably get a new 1377 and a steel aftermarket breech with scope rails for within your budget.