Several metrics involved - area and volume of loft, services in existing cavity affecting other unit(s) especially if there are council tenants also in the building, likely value of existing units, local precedents, likely value of output unit post conversion, condition of existing units and roof, surveys and party wall costs, and legal fees (plan to pay theirs as well as yours). Plan for Southwark to say no to your application at your cost. Plan for tens of thousands if they say yes. Remember they can still say no to some types of conversion plans even when you've managed to buy the loft - so also plan for the most meek of conversions before you do anything else.
Anyone else got any crisper suggestions?