If you let a room in your main home you do need to advise HM Revenue & Customs of this income, however you can claim 'rent a room relief'. The amount of relief you can claim will depend on whether or not the property is in your sole name, but assuming that it is, you can claim a maximum exemption of £4,250 each year. So even though you should notify HM Revenue & Customs of the income, if the gross rents do not exceed £4,250, you will not have to pay any tax on that income.
With regard to the sale of shares, although income tax will not apply, you may have to pay capital gains tax. There is an annual capital gains exemption, which is £10,100 for the current year ending 5 April 2011. When shares are sold you need to take into account the history of the shareholidng from the original date of acquisition to the point of sale. Shares are sometimes bought in lots of tranches, but there are other things such as stock dividends, share reorganistions and rights issues that need to be considered. It would be advisable to seek advice and possibly have a capital gains tax forecast prepared in order to mitigate/minimise any tax that may be due.
Many state benefits are income contingent and you will need to declare the income received if you take a lodger into your main home. Most benefits are not affected by capital gains, but many are affected by the amount of savings you have, so you would need to either discuss your position with someone at your local Job Centre, or alternatively please speak to your local TaxAssist Accountant, who will be happy to help.