Great question! Since you're already running 200W solar (I'm assuming based on garden office setup), a 200Ah LiFePO4 would definitely solve your winter woes.
Worth considering: the actual usable capacity gain @HeathGazer mentioned is spot on, but also factor in your charge controller compatibility. Most PWM controllers struggle with LiFePO4's voltage curve, so you might need a MPPT upgrade if you haven't already—that said, it's a worthwhile investment that'll improve your whole system.
For budget options, I'd honestly lean towards reputable Chinese manufacturers like CATL or EVE cells if you're willing to go DIY, or look at established UK retailers who offer warranty support. The price difference between budget and premium is often just the BMS quality and after-sales support.
One thing I'd add: double-check your inverter's compatibility first. Some older chargers/inverters get finicky with LiFePO4's flat voltage profile. Better to sort that now than discover issues mid-winter!
What's your current charge setup looking like?