I believe there is a plastic connector for exactly this job. Try Screwfix, I'm pretty sure I've seen one in their catalogue. You'll have to measure the size of the lead pipe to make sure you get the correct connector. Plumbers merchants should've been able to tell you all this!!. I find some of them very ignorant and unhelpful!!
Hope this helps
Just done exactly the same on mine. The only way we could find to do it was a lead lock joint (should be able to get from plumbers merchants) to a short run of 22mm copper and then plastic joint onto MDPE.
There is an adaptor available 1/2 NB lead to 25mm MDPE. I would only recommed it as a temorary fix. Why not do the job correctly and have the new plastic pipe connected direct to the service main. You will need a plumber approved by your water supplier to do this. It should not cost to much if you do the prep work. I suspect you want to do the conversion on your property to save this hassle and maybe dig up the pavement to get to the service stop vavle. The water supplier will have specific regulations about the connection at each end and depth of new pipe on you property.
If you do it your self the water supplier will require and inspection by his engineer before you backfil any trench or turn on the supply. The Water Authorities approved plumber can do the connection without another inspection.
I have just had mine replaced aftera ruptured lead pipe .
Yorkshire Water change lead pipe for free presumably because they owe a duty of care to people using their sevices, Thames Water by not changing toxic lead pipes are in my opinion breaking the law. Try either the OFFICE OF WATER SERVICES or Citizens Advice Bureau.