Very little cold water coming out of shower help!

Is the shower for low pressure systems? Also, was it installed correctly as Hot to Hot and Cold to Cold? But the main problem can be the shower is not suitable for your low pressure system. Another thing, is there any isolating valves open fully to the shower, is there a booster pump for the shower, or is there any non return valves in the shower body to be removed if the shower is universal but fitted on low pressure system?

I,m guessing you're is a gravity fed system with the old running from your tank in the loft, it sounds like you need a pump fitting to increase the pressure to your mixer it,s quiet a big job to set it all up ect, so you would need a qualified plumber to carry the work out

Depending on type of shower you have , some showers have a filter fitted at the connection to the shower valve. They can get blocked with scale, or another possibility is do you have a pump fitted as you have gravity system? If not you will need one installing.

If your hot water cylinder is covered in foam blue or green foam or is made of copper then you need a shower pump for a thermostatic mixer it sounds like the shower pump may be the problem

most shower mixers have filters in the connectors check them first, check thermostat is set properly, make sure service valves are fully open.

If you have not got a pump think about getting one installed this will help with your water pressure to the shower.