Instantaneous showers are usually connected directly to the cold mains water supply. Generally tanks don't provide sufficient pressure for them. This cold mains water is then heated as it flows over (in your case) a 10.5 kW electric heating element.
If you have stored hot water in a cylinder with a gravity feed tank, you can fit a booster pump. Positive and negative head pumps are available so location isn't usually a problem. Most showers of this type are fed by stored hot and cold water supplies, and the pump boosts both to ensure a balanced water supply. This will probably be the cheapest way starting at around £600 for a straight forward installation if you employed someone to do it for you, but much would depend upon the work required to modify your existing pipework and electrics. The cost of a basic shower and pump would be about £150 each to buy.
Or, if you have a gravity fed hot water cylinder, you can upgrade it to an unvented type which is connected directly to the cold mains water supply [instead of a feed tank above it] this will provide a better flow and pressure than a gravity fed system [provided you have a decent cold water supply] they can only be installed by a qualified installer and require an annual service, but this can be done at the same time as your boiler. If I had to guess, I think the cost would be 3 or 4 times more than a new shower and pump. Someone who does this for a living would be able to give a more accurate figure than me.
A combi boiler is another option, although generally not recommended if you have more than one bathroom. They can generate hot water directly from the mains as your instantaneous shower does now but have a heating capacity much greater than 10.5 kW. generally a new boiler and install would be £2000 to £3000.