Build a speaker using studio monitors

I'm sure you can do what you're asking. You can find subwoofer plate amps many places. For example, Parts Express Plate Amps

Find a subwoofer you like, something like this- Tang Band Subwoofer or one of many others.

The main issue, in my opinion will be power if you are intending on not using AC. You'll need a hefty battery source to play this for any amount of time. With the subwoofer I linked, you would need a .33 cubic foot (internal dimensions) added to the two Tannoy monitors. You might be able to build smaller enclosures for them, so that could help with the size.

There are plenty of other woofers and subwoofers you can use. I just posted a suggestion.

Mike