Ah, 300 - 350 GBP you say? In that price range, pull the trigger on a
BK Electronics XLS200. If you could bump up your budget a bit, one of their
ported Monolith subs would give you greater output.
When considering room size as it relates to choosing a subwoofer, take the entire area to be pressurized into account. 4 meters x 4 meters x 2.5-to-3 meters = 40 to 48 cubic meters, around ~1500 cubic feet. Assuming the kitchen is a similar size as the lounge, let's double that. 3000ft³ needs something larger than a 10" sealed sub I think. The Monolith would be a worthwhile upgrade, and would give you a much more satisfactory result.
But either would blow both the REL T-Zero and your Yamaha bass modules out of the water.