For the charging circuit I selected the MCP73832 Microchip LiIon /LiPo charger, this will charge at a selectable rate up to 500mA, is very small, 5 lead SOT-23 package and is around £0.40.

For the Boost circuit I selected the Texas Instruments LMR62421 Boost convertor, as these can deliver up to 2.1A, up to 24V out, is a 3mm x 3mm QFN package, and costs around £0.87.

The charging circuit is as follows:

R1 sets the charging current to 500mA, and the LED lights up when charging is in progress.

The Boost Circuit is as follows:

I managed to squeeze the pcb into a footprint of 11mm x 30mm, which should easily be small enough to be directly mounted on the cell, and is not much wider than the micro USB socket.

The use of planes instead of tracks should allow for a large current flow.

I've ordered the PCBs from SeeedStudio and am now playing the waiting game, hoping it works!