Anvil loppers are the ones where a blade comes down at right angles onto a steel pad, so you are in effect just cutting with one blade. By-pass cutters are two blades, like a pair of scissors.
Our loppers are the latter, and they are very efficient, but wouldn't be able to tackle a 2" branch, that needs a pruning saw, which is a one-handed tool, usually bowed, and with which you can fairly easily locate a place on the branch and give it a severe haircut in no time!
Most DIY places will stock them, and a quick check shows that an extending pair from B and Q costs less than £20.00.