This is my first time posting here, so my apologies if my question doesn't completely follow the guidelines.
For some background I am based in the UK and have been working in my first "career" job. I work for a small company where there isn't really a HR department and I directly report to 2 managers. I am not on a written contract (it was a mistake not to sort out before, I know). As this is my first career job I am still very new to the professional workplace. At the moment I have tried working from home one day but I am struggling a lot with concentrating on work with my current situation.
Within the last few weeks I have been applying for new jobs and been going to interviews with prospective employers. Recently an immediate family member passed away and I have been on bereavement leave from work. I have also just got a reply from the company I was interested for when I was interviewing and they have offered me a position which is much more local to me and offered more pay than I had asked for during the interview process.
Without getting into to many details have also had other news (bereavement related) meaning I am planning to leave the country soon for a week to be with family.
The problem I am having is how to handle my current employer, because over the next week I have bereavement things to take care of with my immediate family which will require me to not work for another 2 days.
What I am unsure about is how to leave my current employer. Although personally, my family business always takes priority, I feel bad to leave my current employer without a developer without notice as we are a small development team and I guess that my actions would be seen as unprofessional.
What is the most appropriate way to leave/discuss with my current employer based on my situation?
Should I tell my potential new employer about my current situation? (I think if I leave soon I would burn bridges with my current employer and this is my first career job and only reference)
UPDATE
Thank you for the advice. I spoke to my Manager a day after the advice and explained my situation and that I would be leaving (along with my written notice). To make everything as easy as possible for the transition I offered to write documents for the hand over during some agreed hours at work and some at home on the weekend. I also done some development on the weekend to wrap up my last main project. My manager and main boss of the company has been very understanding and helpful during this time.
I also mentioned my situation to the new employer before I sent them back the signed contract, they was also very understanding and said I could have some personal time of.