Absolutely not: its not because the preceding months were rather cold that the following months will be warm... This is basic probabilities.
Indeed a 5 degrees below average months can come in the middle of two very hot months, even if the chances are very small. More importantly, there have been many examples through out the past of very cold winters being followed by very bad springs and summers: in France for example, february 1956 was the coldest of the 20th century with an average temperature over the country 10 degrees below average. March 1956 was cold in france, april also, may saw wintery showers, june was one of the coldest on record, july and august saw windstorms and rain on many occasions and people had to wait until september to a last get some good weather. Same thing happened in 1963, with the coldest winter followed by a cold spring and summer in France. 1979, 1985, 1986 and 1987 all saw cold winters with severe frosts, and all the following springs and summers were notably cold over much of Western Europe.
In fact it seems that many of the coldest winters over Europe between 1950 and nowadays were followed by a persistent cold weather pattern over Western Europe [same thing in 1954 also, with a very cool summer in France].
It will be interesting to see how this year will come out, as for now a part from a very mild spell in the second half of march and another one end of april, the weather has been mostly cold and sometimes even very cold over much of UK and France, all this thanks to a very unusual dominant weather pattern: how long is this going to last?? Because as long as it does, no notable warm and sunny periods will be seen over Britain.