No, building regulations require that rain water and foul water are kept separate and that only foul water can go into foul water drains and likewise for rain water drains.
The problem that you have is common in that about 50% of mid terrace houses, in that there is no rain water drain located in the property as the gutters located at roof level discharge into down pipes located in adjoining neighbouring properties.
The first thing that you should check is to see if the rain water drain runs under the grounds to the back of your property. If this is the case, your best option is in most cases to connect directly into this rain water drain.
However, if there is no rain water drain in your property, the other more expensive option you have is to build a soak away in your back garden. The size and location of the soak away will be determined by the size of your garden, the size (meter squared) of the roof over the extension, the size of the soak away and its infiltration into the soil in the back garden.
In cases like this, It is quite common that builders discharge the rain water into the foul drain. This will eventually catch up with you when you go to sell the property and a certificate in compliance with building regulations will flag this issue or may come to the attention of the local planning authority when drains are being unblocked.