A pumped shower will do the job. Some are inexpensive. They can get noisy, get one that only runs when the shower is in use. If you can mount it on a board padded with felt or rubber, with a box round it, this will muffle the noise.
Raising the cold water tank on a platform might not be necessary, but measure the one you have. It is very important that the pump does not suck out all the water and run dry while you are showering.
A typical hot water cylinder holds about 100 litres. In summer, it's possible you might use an equal amount of cold. So I'd look for a 200 litre cold tank (or two smaller ones connected with a large pipe at the bottom by a skilled plumber. You draw from one while filling from the other to keep the water fresh.
Aqualisa showers are very good quality.
Don't get a bar shower. For some reason they are not as good or as durable as round ones.
Before you spend a lot of money, find out what the water flow to your house is. Fill a bucket at the kitchen cold tap, and the garden tap if you have one, calculate litres per minute. 20lpm is good, 10lpm is bad. Older houses often have small pipes and poor flow. Flow is not the same as pressure. A combi cannot give good HW without a good flow and pressure.
A cold tank can give good flow (with big pipes) but poor pressure.
If and when you get a new boiler, you can upgrade to an unvented cylinder, which gives the best HW, better than a combi, but you will need a good incoming flow and may need to replace some of your old pipes, including the one coming in from the road. This can be easy if you have a garden you can dig up, and wooden floors with a space underneath. Or difficult if you have a lot of concrete in the way. If you do it, you will be glad you did.
Modern houses with blue or black plastic incoming pipes tend to have good flow. Flats and converted houses may be almost impossible to improve.