Small lump sum saving

So I've finally got my budgetting under control, and now I'm looking for something to do with the small amounts of cash I should have left over at the end of each period. Currently, that period is every 2 weeks as that's how often I get paid, and it makes most sense to match it. Some periods, I'll have some money left over, but some I'll go over my budget (unavoidable, my mortgage is over half my regular wage). My plan is to work out how much I need to leave in my regular account to cover the next period (if it goes into deficit) and move the rest off into a different account, but one I can get to easily enough.

So I need an account that I can move small lump sums off to on a semi-regular basis (something with web access would be ideal), where they earn more than the probable 0.1% I'm getting currently, and where in the event that I go over budget in any period, I have instance access (7 days at the outside, as I hope to know pretty quickly when things are going south)

Does such an account exist? I'm thinking that I need to keep it in-bank for those credit transfers, so I'm limited to TSB but their non-notice accounts are pretty poor.

If you have 7 days to know that you need cash then "in-bank" is not really required. Check out these:

[broken link removed] (Discuss)
3.10% on €1 minimum to €100,000
2.80% on €100,001 to €1m maximum
Note 1: Instant access
Note 2: Interest paid annually.
Note 3: If you balance is above €100,001 then 2.80% applies to the entire balance.
Deposit Protection: Irish Government Bank Guarantee Scheme until September 30th 2010, Irish Deposit Protection Scheme only from October 1st 2010.

[broken link removed] (Discuss)
2.00% on €1 minimum.
Note 1: Instant access.
Note 2: Online only.
Deposit Protection: Dutch Deposit Guarantee Scheme
Deposit Safety: As RaboDirect's parent is the AAA rated RaboBank, deposits are generally considered very safe.

Tks username. I think my main concern with going external to my bank is the short period of time. For ex, the current period ends tomorrow, and the next one runs from 14/5 to 27/5. So I can move all my money off to my new account on the 14/5. Any bank-to-bank transfer is going to take a couple of days to clear, so my new account will only show it middle of next week. Then on the 21/5, I realise that my spending is out of control and I need an extra 500 to cover the period. Optimistically, if I request the transfer on the friday, I might get it by the following Tuesday/Wednesday. In the meantime, a bunch of DDs come in and things go pear shaped.

If it was a monthly timeframe, I'd be more comfortable, but getting money out, and getting it back in again within 2 weeks I think is bordering on unfeasible. Maybe I can delay the transfer or combine 2 fortnights into 1 and take that period as a whole?

billy-bob, what about the AIB regular saver, rate is currently 3.5% gaurantee to be 2.5% above the ECB rate - instance access to money, etc - check out the savings best buy page.

I don't think I'll be able to do any sort of 'regular' savings plan, as I won't know from month to month how much surplus I'll have, it could be anything from 100 quid up to 800.

Well, if you dont want to go external, the accounts on TSB website are your only options....

I didn't say I didn't want to go external, username. I said I didn't think the period timescale would allow me to do it properly.