There are plenty of MR16 LED lamps available, just google them. You will need to have compatible drivers for LEDs and the load ratings for the drivers will need to be suitable for the lamps also. the existing one in the fitting may not be suitable.
It is the integral electronic transformer which will determine what can be used. They are not simple transformers but turn AC to DC then back to AC at high frequency to transform down then use a switch mode system to regulate the output. This means they have both a maximum and minimum supply current. Any replacements lamps must fall between the two limits.
So if it says for example 10-50 VA then you can go down to 10 watt. As far as you need to know VA is same as Watts.
OK dichroic means that light is reflected but heat goes through the reflector so the item the light is pointing at does not over heat. With LED you can forget it as so little heat generated. I have just got some 9 LED MR16 0.58W/12V lamps for my bathroom from Pound World sure you can guess the price each. However these are very low power lamps and with the GU10 version of the same lamps they will not switch off. They go very dim but not off.
If the supply for the MR16 lamp is from a simple transformer as in my case no problem but if an inverter is used then likely these would be too small.
So really you have to find the dropper box and read the info on the box. As already said if there is a minimum then likely you can't use LED. A good indexation is real transformers are large and heavy but inverters are small and light.
Although you can replace the inverter for an LED driver likely best option is to change to GU10 instead of MR16 and feed the lamp with 230v instead of 12v this will also mean cold cathode can also be used.
As a PS found this add http://www.tlc-direct.co.uk/Products/PWMTS52.html I would ask them what lamps will work as they seem to be a good supplier. Seems to say LT MR3W is a related item at 3.7 watt but I would ask to be sure what the minimum size is that the lamp can take.