If I give in my notice of leave, am I still entitled to reimbursement on expenses owed? The arrangement is typically a month gap so expenses incurred in this month are paid at the end of the next month, and I am worried that if I did wish to leave, any significant expenses may not be reimbursed by my employer, such as travel costs for fuel, parking and tickets for off-site (not at office) work.
Generally they should still reimburse you for those expenses with a few conditions:
They will want you to submit them as quickly as possible, that way they can contact you for questions while you are still an employee. Turn in as many before giving notice to reduce the backlog
They will only cover things through your last day. Which means that they may only pay for part of the monthly parking pass, or part of the train ticket. Understand how much you are putting at risk before giving notice. It might be cheaper to skip the monthly pass if you will only be parking for a few days of the next month.
If your leaving will invalidate some pre-paid items (tickets, registration fees) they may want compensation. You need to discuss this with HR.
Be aware that they may require you to payback any money paid for moving or tuition if you signed paperwork that obligated you to pay them back if you didn't remain an employee for X months after they paid the expense.