Sorry, have never used Skype, but have used a mobile network for ~21 months. I'd have thought that for reliability you might prefer to use a mobile (Asda PAYG costs 8p per minute for calls to 01/02/03 landlines, and Skype is perhaps mostly going to offer you calls to friends/ relations rather than business calls, at a guess).
How long do you expect to be without a landline? Only ask because you can find people offering SIMs on Ebay for Three, Vodafone and probably other networks. The differences can be quite major though - on Vodafone, someone might charge a tenner for 1 GB of data, while a PAYG SIM for Three may cost 9 quid or less and be for 3 GB for 3 Months, whichever gets used up first.
If the postcode for where you are going has Three as an option, it might give you a breathing space to connect up a laptop or PC using a USB dongle. Getting a dongle with 1 GB of data is 30 quid from the online Three store, and then you could get a further 3 GB via Ebay. (Three sells a dongle with 3 GB of data for 40 quid, so each GB is roughly 5 or 6 pounds compared with 3 or less off Ebay).
Or consider a Three MiFi (combination that uses SIM and mobile network to offer internet access and a wi-fi access point for your laptops/mobile phones to use). You can then add 3GB/3month SIMs as often as you need buying them on Ebay at lower price than top-ups in a Three store.
Other networks may offer better options - there used to be SIMs for Vodafone where any data credit was not wiped at end of a month but new SIMs apparently only have data allowance for a month.
Worth checking the options for all mobile networks for your new location.
PS If you do choose to use Asda mobile, they use the Vodafone network so check coverage on Voda and either use a Voda mobile phone, or get an unlocked phone (Asda Living sell a range). If you buy a 5 quid top-up voucher you can get the Asda SIM pack free, so each time you top-up you can check to see if you get a nice "memorable" number in a new SIM pack (and flog the SIM on ebay !