Is it safe and legal to convert an immersion heater circuit for lights and outlets?
16 amp MCB (not RCD) supplying a socket - OK
fused connection unit with 3 amp fuse to supply light - OK

However, there are two important issues:


The cable size. A standard radial socket circuit uses 2.5mm (minimum) cable on a 20A MCB. Sometimes (say pre 1980) immersion heaters were wired assuming a 2kW heater on 1.5mm cable. Before extending that circuit, you'd have to verify by calculation that 1.5mm cable is adequate for a 16A circuit. As a general purpose socket circuit the design current for the circuit would be the same as the protective device (16A)
RCD protection. All new sockets must be RCD protected; all new cabling must be RCD protected (unless metal-sheathed cable or in metal conduit).


If the existing circuit is not RCD protected, you should add RCD protection. If you can't add an RCD to the existing consumer unit, there are ways round it (such as an RCD in a DIN rail enclosure next to the consumer unit, or an RCD fused spur, but if your consumer unit is that old it's probably due for replacement.

Don't reduce circuit protection down to 6A at the MCB - there is no need, and fridges/freezers can have high motor inrush currents.