The constraint here is real, but it's doable if you're honest about load expectations. I've run a similar setup on my shepherds hut before upgrading.
100W rigid panel (Fogstar or Renogy) gets you about 300-400Wh on a decent winter day, less in December. Pair that with a basic PWM controller (£20-30 used, or new Victron SmartSolar 75/10 if you stretch) and you're looking at the numbers @DaveMoore70 mentioned.
The hidden cost most people miss: battery. A decent 100Ah LiFePO4 would blow your budget instantly. You'd need to work with whatever lithium or lead you've already got, or invest in a small 48V or 12V battery bank separately. If you're just topping up a phone and keeping a fridge running intermittently, a 50-100Ah lead battery (£40-60 used) is realistic within budget.
One thing — don't scrimp on wiring and breakers. £15-20 in proper marine-grade cable and a