The problem with the June Night Sky in UK latitudes is that there isn’t much of it! Many observers write off June and July as observing months, and concentrate instead on doing that equipment maintenance/upgrade that’s been nagging away at you all winter. It is certainly true that if you want very dark skies at this time of year you will only get them at very unsociable hours (about 12 to 2 am BST) and then only near the zenith. But that can offer some fine observing – indeed I had a couple of good midnight sessions with Dick Phillips on midsummer’s night itself.
It is also your best chance of seeing noctilucent clouds, typically near any glow from the sun below the horizon.
One possible observing opportunity this month is an occultation of Mercury by the Moon at around 1pm on 26 June. But the Moon will be a very fine crescent only 10 degrees west of the sun, and all the usual warnings of the risks of looking near the sun with any any kind of optical aid (or, indeed, at all) apply. Don’t do it, unless you have a foolproof way of keeping yourself safe, and you know what you are doing.
One method that can work, if the buildings near you allow it, is to place yourself and your telescope just in the shade of a suitable tall building, but still able to view the relevant patch of sky, in this case about 10 degrees west of the sun. You will need to remember to keep moving both yourself and your telescope to stay in the safe zone as the sun advances around the sky. But it will be very difficult even to find the moon, let alone Mercury, in the glare of the bright sky. Do it safely if you try!