What about prevention? Rather than hand wringing and making a blanket statement about eradication of borders, why not be a force for good?
Petition the UK government to stop selling arms to KSA, which are then used to bomb the shit out of the poor Yemenis.
Make waves about the GERD project. If you are concerned with famine and the displacement of native populations this brings, this should be a big issue for you. We're staring in the face the potential for Egypt to be starved of water. There's your next refugee crisis, but only the USA cares at all.
The reality is absorbing a large amount of individuals with different languages and religions will always cause issues on the ground. How will you educate them? Provide enough interpretation services to allow them all to access services we take for granted? Provide housing, health care, and psychological services? How about more mundane issues: where will they pray? There are areas of this country where there are no mosques. This pushes Muslim refugees to areas which are densely populated.
The harsh reality is that we can't save them all. That we won the birth lottery. There is only so much we can do on an individual level. Governments need to make fundamental changes to their arms and diplomatic policies in order to deal with the underlying issues. Elect better leaders, run for office yourself, start or engage with charities where the money is used appropriately rather than paying CEO salaries.
Sadly, a blanket policy of letting everyone in will just end with a slide in our own standards at home as services reach breaking point. Having this discussion at all is from such a place of privilege. We think nothing of allowing others to use our services or move here because we can't envision a world in which we won't have these things.