I cannot imagine any aerodrome can be operated to a financial profit by the sole payment of whatever landing fees from recreational pilots. Either a lot of volunteer work is required, as is usual at club aerodromes, or the a/d must have sufficient income from professional operators.
How many landings "from outside" per weekend at the typical recreational airfield? At perhaps 35 flyable weekends per year? How much yearly revenue at what landing fee?
Whether 10£ or 50£, the contribution to the total yearly running cost will be marginal.