The United Kingdom has a Pay-as-you-Earn (PAYE) system. In most other countries, this is called Pay-as-you-Go, and in the USA it is called withholding. Income is withheld from employee's paychecks, and is transfered to the government by the employers on a regular basis on their employee's behalf.
Different countries have different guidelines that determine how often taxes are paid. In the UK, it is a function of the average monthly check to Her Majesty's Revenue & Customs (HMRC) that would be sent by the employer. If it is low enough, they only have to pay the taxes quarterly (in the USA, businesses file taxes quarterly).
The UK, just as in the USA, uses taxes it collects to pay for current expenses. Any delay would be a function of when your employer electronically transfered your monthly/quarterly PAYE income withholding, or when a particular government expense needed to be paid. With few exceptions, taxes are placed in the general fund to be spent on whatever the government desires. For more information about how your government spends your money, see this graphic.
Department/ organisation 2010/11, £bn 2011/12, £bn % change including inflation
TOTAL SPENDING 689.63 694.89 -1.58
Department for Work and Pensions (DWP) 160.08 166.98 1.88
Department of Health (DH) [See note] 105.45 106.66 -1.2
Department for Education 58.28 56.27 -5.7
Debt interest payments 43.30 48.20 8.73
HM Revenue and Customs (HMRC) 45.78 46.59 -0.61
Ministry of Defence (MoD) 38.12 37.25 -4.55
DEVOLVED SPENDING SCOTLAND 34.53 33.52 -5.18
Communities and Local Government (CLG) 37.60