OK, how long does it need to run from on the battery pack, and under what load - what is it driving?
eg. Something that only needs to run for a few seconds occasionally has very different requirements to a pump, grinder or whatever than may need to run at high load for long periods.
That gives some idea of how big the battery pack would have to be.
eg. Something like this would give roughly around 60 - 90 minutes at full load, much longer at light loading:
**broken link removed**
Those need a special charger that costs probably another £30 or so.