I want to know what is the best time to buy Euro Currency, from GBP,
for two separate trip in early and end of June ?

Considering currencies prices fluctuate according to a random pattern,
this question does not have an answer.

However if we consider that the Euro has been losing against the pound
for the recent past, then NOW would have been better than 1 month ago
for example. This does not mean tomorrow will not be any better.

Considering the incertainty, the best approch is therefore to buy in
small amounts every days until the trip starts. This will cost
transactions however.

Cheers

Emmanuel

Quite right, you cannot anticipate the market, just maybe have good luck.
For most travellers, the actual difference in price is really not a
significant amount  - despite the personal disappointment of finding
that one might have bought the foreign currency for less a day later. 
I equate it with the situation of buying petrol for one's car:  how
far out of your way will you go on the chance  - not the certainty - 
that you can get it cheaper somewhere else.

Generally, the transaction costs on changing currencies is more
significant, especially for smaller amounts, so it is cheaper to buy
cash in larger amounts.
It is also sensible to use a credit card.