Will the coronavirus restrictions be lifted soon? I will also be traveling this July to UK I hope things will be fine by July in London?

nobody is certain. but it seems we know enough now about The CCP Virus to accept that a) it's not going anywhere. it will be back in Fall and b) it's far less deadly and even far less disabling than we'd initially thought. and we have c) proof in countries like Sweden that didn't do full Lock Downs that Lock Downs are entirely ineffective at reducing death rates (i think you could competently argue, although i wouldn't, that CCP Virus deaths are an insurance scam and few of them actually exist at all).

i would expect Lock Downs to lift toward The End of June. Possible a couple weeks Sooner.

No one knows yet. While restrictions are easing in many places, the number of active cases is still increasing daily in both the US and UK. The easing of restrictions may result in a further increase in cases. I wouldn't count on international travel in July, but it could happen.

Even if travel restrictions are lifted, they'll be 2 weeks quarantine period before you are allowed to move around

The UK government is expected to announce today that anyone travelling to the UK will have to quarantine for 14 days as part of measures to prevent a second peak of the coronavirus pandemic........ national events that normally happen in July, August have been cancelled, hospitality industry will be the last to go back to normality that includes restaurants/cafes/hotels  so I doubt in 8 weeks you will be flying as you will have no where to stay and so can't quarantine for 14 days.......... ONLY emergency travel is advised and a hoilday is not emergency

Nobody knows. However, there is talk of a two week quarantine for travellers to UK!

 I would forget about a trip to the UK. You will need an address for 14 days
lock down.

I'd suggest moving your trip to next year; even if you're allowed into the UK, you can expect to start with a 2-week quarantine period, and nothing to be open when you emerge fro mit.

Here's a quote about the situation in Sweden: "Cases of the novel coronavirus in Sweden have reached at least 23,918, with its death count at 2,941, as of Thursday, according to the latest figures from the country's health ministry."  They are NOT doing well, and other countries in Europe are likely to continue the lockdown for quite a while.