Croydon is one of the more permissive London boroughs for renewables — most of it operates under standard national permitted development rules — with one specific and unusual exception that's worth knowing about before you get quotes.
Croydon has around 19 to 22 conservation areas, of which only 3 carry Article 4 directions: Chatsworth Road, The Waldrons and Kenley Aerodrome.
Chatsworth Road is genuinely unusual in a London context. Most Article 4 directions restrict "alterations" in general terms, and whether that captures solar is a matter of interpretation. The Chatsworth Road direction names solar photovoltaic and solar thermal installation explicitly. There's no ambiguity to argue about — if you're on Chatsworth Road, budget for a planning application from the outset rather than hoping permitted development applies.
Everywhere else in Croydon, including the other conservation areas and the great majority of the borough, standard national rules apply. Croydon does operate a borough-wide HMO Article 4 direction, which is irrelevant to renewables but will cause some address-checking tools to report a restriction on every Croydon property.
Croydon is one of the better London boroughs for retrofit economics, and the reason is simple: a large stock of inter-war and post-war semi-detached and detached houses with side access, decent gardens and substantial unshaded roof area. The 1-metre heat pump boundary rule that dominates inner-London terraces is rarely the deciding factor here.
The southern end of the borough — Purley, Sanderstead, Coulsdon, Kenley — has larger detached plots where ground source heat pumps become genuinely worth pricing rather than dismissing on space grounds, which is unusual for London. Elsewhere air source will still be the sensible default.
Much of the borough's semi-detached stock was built with unfilled cavity walls. If yours hasn't been done, cavity wall and loft insulation will pay back several times faster than any generation technology, and will reduce the heat pump capacity you need to buy.
For costs, grants and how the national rules work, see the heat pump guide, solar guide, air conditioning guide and insulation guide.