My willingness to leave a tenancy early would be directly proportionate to the amount of effort I had put in to find it and furnish it. Extreme example:
2000 miles on the road
6 weeks
1.5k van hire over x3-5 weekends
1-3k worth of white goods
2-3k worth of furniture, curtain rails, curtains, bathroom goods etc that would only fit in that house and possibly not the next one
1k of gardening equipment
So, if a LL offered me one month's rent rebate there's not a chance of getting me budged until I can find a house that my just-bought stuff will fit into, unless the LL was overing to reimburse me for the entire lot, should I only be able to find a house that already has all that stuff installed and there's no room to store my old stuff in (sure, you can sell it, but a £1200, six month old range cooker will only sell for £300 outside of large towns and cities).
I say this with authority because I've had to do it twice in three years!
Hopefully yours is a normal flat where everything was supplied and they just moved from down the road.
Also, you should be aware that if you give them notice now, this is precisely the time LL's put their rents up by 10-25% and they generally don't start sliding down again til September (although I have to say the market is pretty bad this year and I've seen a ton of reductions as early as April and May, for the first time in years).
So, if they have to pay a higher rent, you need to think carefully about what you should offer as a move incentive.