It would likely depend on the precise result of the election.
Of the major parties only the Liberal Democrats have consistently and officially voiced strong opposition to Brexit in principle. Up to the point where the election was called they have been mostly arguing for softening the terms of Brexit. It is fairly unlikely from current polling that the Lib Dems would win an outright majority but if they did there is a good chance that they would see it as a mandate to reverse the process (if that is even possible now) as this seems to be the central platform which they are campaigning on.
It is more likely that they would end up as power brokers in a potential coalition (again) in which case they might well make having a second referendum a condition.
The Labour party at least officially was opposed to Brexit in the referendum campaign but their actual campaign sent rather mixed messages and this has certainly been a point of tension between the leadership and parliamentary party. Subsequent to the referendum they seem to have regarded it as a done deal and have tended to support the government on the issue overall eg the leadership supported the vote to trigger article 50.
Also the Labour party is in a bit of trouble at the moment, polling very badly indeed and has a fundamental internal rift and it seems that a pro-Brexit line is likely to play better with their target electorate plus the leadership seems fairly ambivalent on the issue.
Although it is not terribly clear what the actual mechanics of the policy of a potential Labour government would be (ie they have a lot of ideas on what they want to achieve but not how to achieve it) it seems likely that they would adopt a much more interventionist approach. For example on housing their ideological position suggests that they would try to build a lot of new council housing. They may feel that it will be easier to do outside the EU, this would certainly be the case if they decided they wanted to subsidise industry.
Oddly UKIP are a bit of an unknown quantity, given that the conservative party is now firmly on a pro-Brexit course 'independence' is no longer a unique selling point for them and their new leadership doesn't have the same high profile that Farage achieved. Having said that they could potentially take away socially conservative Labour voters.
The SNP are firmly pro-EU but this is tempered by the fact that they might see Brexit as a way to leverage Scottish Independence.
It is also not entirely beyond the realms of possibility that Labour MPs could defect to the Lib Dems en mass or stand as independents on an anti-Brexit platform.
In terms of the strategy behind calling the election it seems likely that the Conservative leadership has two main motivations. Firstly that they see this as an opportunity to increase their majority at the expense of Labour and UKIP both of which are now in rather awkward positions and secondly that the current leadership has inherited a bit of an awkward position themselves in that they are committed to a process which is both diplomatically and politically potentially very difficult and dangerous and if it all goes horribly wrong they are really out on a limb so if they get a fresh mandate they can at least blame the voters.
There is also a bit of a suspicion that, although leaving the EU made a really good political rallying cry, very few mainstream politicians really wanted it to happen as nobody really knows what the consequences will be and politicians are naturally averse to real world consequences which can be directly attributed to their actions.
Here Labour may feel that they have a bit of a cushion in that they didn't start the process and can always claim later that it was out of their hands or if it is obviously going to be a disaster they can put the brakes on and say that they were opposed to it all along.
The Lib Dems have little to loose on the issue and a lot to gain as getting the anti-Brexit camp to break party lines and vote for them would be a big win. Indeed this has already happened to some extent. So it seems like their best position is to campaign on a firm Brexit-sceptic platform and stick to it which is basically win/win for them as they either lose and have to do nothing or win and have a mandate to do what they want.
