Buying a gaming laptop is full of complex choices, some of which like the feel of the keyboard and nuances of the display don't necessarily have a right and wrong answer and are more up to the individual.
To get a decent gaming laptop that is cheap (on a budget) you want to (in order of importance):
1) get one with a discrete (separate) video card [Intel integrated graphics are NOT discrete cards]
and, if you can afford it (this will be out of your budget range this time)
2) get a laptop with either a 7200 rpm hard drive or a much faster SSD
Option 2) without Option 1) will be near worthless. You need a decent, separate video card period.
Here's two options from the Amazon UK site:
This one has a nice Intel CPU and a Geforce 710M video card. While the 710M is hardly a powerhouse, it's going to be better than most integrated graphic solutions. This one (I'm guessing) you'd only be able to raid with low settings, maybe solo with medium/medium low settings in LOTRO.
For 50 pounds (if that's the right terminology) more, I'd highly reommend this one (from a hardware perspective, not saying you'll love the keyboard, etc):
This one has the the Geforce GT 540M video card, which is going to be a lot better than the 710M (pay attention to the last two digits '10' vs '40', not the first digit. You'd probably be able to raid with medium to medium to low settings with this. Maybe even solo with medium to high settings.
I highly encourage you to shop around. If you simply get a laptop that has a true discrete video card, you can't go completely wrong hardware-wise. From there, get the best discrete video card that you can afford. If you can snag a model with a 7200 rpm hard drive (versus the 5400 rpm that most cheap laptops come with), you'll see a big increase in load times and slightly less perceived lag in LOTRO. However, my current gaming laptop has the slower 5400 rpm hard drive, and it's not a big deal, I play LOTRO and StarCraft2 on high to ultra high settings because I have a decent video card (Geforce 560M).
other favorite middle-earth games: The One Ring RPG by Cubicle 7; LotR: The Card Game by FFG; Hobbit/LotR Strategy Battle Game by GW