What should happen is that the UN should take control and force all countries including neighbouring Arab countries to take on their fair share of refugees (families get a priority). UK like Germany should also take in their quota of refugees - probably equalling 800K or more - for this round - no doubts there will be additional rounds moving forward as the precedent will have been set.
What we should NOT entertain is the chancers from Calais or the ones that are forcibly trying to break borders - they are not refugees, they are migrants and potentially criminals.
As for the impact on the UK - most definitely put more pressure on the finances of the UK as unlikely that most of these people will work or be allowed to work legally. Will reduce the quality of life for all - which is not that strenuous considering that we seem to be living unsustainable lives in any case - we can afford to change with a bit of compassion.
Expect an impact on the benefit system and social housing to reduce the share per claimant both genuine (which will be a shame) and for the benefit cheats (which I personally would like to happen).
This will then force a major overhaul of the welfare system, including NHS, hopefully unions, social housing, benefits, JSA, etc - which again is desperately needed - somehow even stop the free movement of people between the UK and Mainland - they will find a way to force this though.