I guess that by "eastern block countries " Barrie means ex Soviet satellite states (or Iron Curtain countries if you prefer) which are now EU members.
As far as I can see Jane is correct that something like 98-99% imported dairy is from the EU (her comment is very similar to this report on the possible impact of Brexit on the dairy industry.
Looking at the sources within the EU the largest are France, Germany and Ireland
Belgium, Denmark, the Netherlands and Italy make up about another 15-18% so the “eastern bloc” can only be less than 1/6th (maybe 13-15%) of our imports - I can’t see them skewing the market much.
About 90% of our dairy exports go to the EU - under WTO terms the average tariff would be 18% (plus there would be a tariff we’d have to impose on imports) but it is up to almost 80% on some products - that makes UK produce much less competitive in the EU which is our single largest market.
See also https://projectblue.blob.core.windows.net/media/Default/Imported%20Publication%20Docs/Horizon/Horizon_Dairy_Bitesize_Brexit_20190417.pdf for more explanation of our dairy industry than you could ever need