How can i download old points of interest data from openstreetmap?

Using a "history" file will get you there but you will not see the data that was removed during the license change. A slightly more complete approach is using one of the very old "planet files" from http://planet.openstreetmap.org/cc-by-sa/ and processing that. These files will have an older data format and you'll have to download version 0.35 of Osmosis to process them.

However, whatever way you choose, this will not give you any indicator on how many POIs there were in London at the time - just how many POIs OSM knew about! So if you intend to compute something like "the number of pubs in London has changed so-and-so over the last 10 years" then forget OSM as a data source. OSM's coverage of POIs in London in 2007 was patchy at best - counting, just to give an example, about 900 hotel/restaurant/pub POIs compared to today's 21,000.

You can use osmium-tool along with a full history file (*.osh.pbf) of UK (country extracts are available from Geofabrik) to make a normal non-history OSM file "snapshot" at certain timestamp. Osmium-tool can also clip it to London area and filter POI you want (e.g. shop=*, amenity=*) so you could load it in JOSM, for instance - or whatever can read .osm or .pbf files.

(Sorry I have no time to explain each step, but the above way will certainly work. ;-) )