Decent software or websites will show you the relationship betwen a share price and the FTSE as beta. This can vary about 1.0, this median level expressing a 1% rise in the FTSE as a 1% rise in the share. Sharescope will do this for shares, sector indices, anything listed really. Beta values can be above 1 or below 1 but you should be aware of the time period over which this is being judged.
I do believe that if you create a portfolio of only the biggest cap 20 FTSE100 members you will track the FTSE itself to a very high percentage. Certainly adding in the 250 additional shares to the FTSE100 to make up the FTSE350 makes very little difference.