Stolen BRP but Resigning From Job- Can I travel?

[Skylar1331]

I am resigning from my job on November 28th on which date my employer will be contacting the UK Home Office to let them know that I will no longer be sponsored by them. I have to give four weeks notice so essentially I will be working right up until Christmas. I am an American citizen on a Tier II visa which I just switched to from Post Study Migrant a few months ago.
Unfortunately, our house was broken into a few weeks ago and my brp was stolen. We reported it to the police that morning and have the crime number and documentation etc. and I just today notified the home office. Because I am planning to cancel my new visa when I leave my job, do I need to apply for a new BRP? I'm currently looking at jobs in the EU and do not want to risk sending my passport away for so long if I will not need the new permit.
More complicated still is that my partner of a year and a half would like us to spend Christmas at his mother's house in Liverpool. I would like to be able to get in and out of the UK to interview with potential employers over the next few months and will be packing up our house and putting belongings in storage on Dec 19, spending Christmas with his family and then hopefully re-locating to Europe for a new start.

Questions:
1)If I have not yet submitted my letter of resignation and leave the country, can I get back in without my BRP? (I've spoken to my employer and they asked me to wait until Nov. 28th to satisfy a project deadline and then to complete my four weeks notice period with the understanding that I can be absent to look for new work in the meantime.)

2)I have travel booked on Nov. 22nd. If I submit my letter of resignation early can I leave for this travel and come back without my brp?
3)Can I use a change of circumstance form to notify the home office of the situation?
4)Is there a help bureau I can go to in London? Someone said I could explain my situation and get some help from the Home Office if I went to a help desk near Victoria Station?

5)Should I have my partner’s mother write me a letter that I will be visiting her for the holidays so I don’t have trouble getting in and out of the UK after I have submitted my letter of resignation? (My partner is a UK citizen and we can’t go to the US for more than 90 days so we are trying to stay in the EU until we decide what our long term plans are- we don’t want to be forced to marry just so we can co-habitate and I may be pursuing a phd in the fall if the right job opportunity doesn’t come up.)

Any suggestions on the best way to approach this with the authorities? I assume if I leave and try to come back I should have all paperwork sent to me with my original brp, the police documentation of the theft and potentially a copy of the letter of resignation I am submitting?
Any advice would be much appreciated.

[Damanisshallo]

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