remortgage with same lender or move?

[breathe21]

I want to raise some cash on my investment property, have a mortgage of £98k and prop worth £155k. Rent at mo is £550 but have just had a rental value of £620. I am up to the max amount i can borrow with my existing lender at a rent of £550. My tennant has give me 3 months notice. So I am now going to advertise the prop at £600 per month. Could I stay with existing lender and ask to increase lending amount affordable to the £600 rent or move to another lender, even though I may not get a new tennant straight away. I can get a tennancy agreement with the letting agengy, they find me the tennant but I manage the property myself. Could I do this now or would I have to wait until I was getting the £600 rental income. When the tennant first moved in 3 yrs ago my BTL was all in place and so in theory I got the mortgage before I got the tennant.