It's legally impossible to postpone the election without changing current laws. However, Parliament has been dissolved and thus laws cannot enacted or changed.
The two parliamentary acts that determine the date of the election — the Fixed Term Parliaments Act 2011 and the Electoral Registration and Administration Act 2013 make no mention of delaying the election.
Section 2 of the Fixed Term Parliaments Act 2011 states that:
If a parliamentary general election is to take place as provided for by subsection (1) or (3), the polling day for the election is to be the day appointed by Her Majesty by proclamation on the recommendation of the Prime Minister (and, accordingly, the appointed day replaces the day which would otherwise have been the polling day for the next election determined under section 1).
And the Queen has proclaimed the election to be held on June 8th:
Also, the Brexit Minister David Davis mentioned that the current laws have to be changed by Parliament. However, Parliament has been dissolved which makes it impossible to enact any new laws. Thus, the date of the election cannot be changed.
The Brexit Secretary suggested that, to change the date of the election, the current laws would have to be changed and that was likely to be impossible because there are currently no MPs and no parliament.
As quoted from the official UK Parliament website, business in Parliament will cease when it is dissolved:
House of Commons
MPs are allowed access to Parliament for just a few days in which to remove papers from their offices. The facilities that the House provides for MPs in Westminster during a Parliament are no longer available to them from 5pm on the day of dissolution.
House of Lords
Members of the House of Lords retain their positions, but all business in the House comes to an end when Parliament is dissolved.