Can I transfer investments to my partner?

Yes, you can do this. What you will need to do will depend on teh investments that you wish to transfer. Provided that they are transferred without a payment of a consideration of money or money's worth there will be no tax to pay on the transfer.
Several sections of the HMRC webiste cover this and say:
"There is no chargeable event and so no gain when the owner assigns all of the policy rights to another person but receives no money or money's worth in return."
"Any transfer of an asset between a husband and a wife or between civil partners of each other who are living together is treated, with certain exceptions, by TCGA92/S58 (Taxation of Chargeable Gains Act 1992 Section 58) as taking place for such consideration as will give neither a gain nor a loss to the transferor."
"Gains from life insurance policies, life annuity contracts and capital redemption policies are taxed as income. A charge to tax on a gain may arise when a policy or contract is assigned for consideration. However, no gain arises and there is no tax payable on an assignment between spouses who live together at any time in the year of assessment in which the assignment takes place."
In terms of what is required, it depends whether you are transferring an investment or assigning it. So for example a share or investment trust would be transferred to your wife by way of a simple CREST transfer.
Unit trusts will be transferred by completion of the relevant form from the Unit Trust provider or the platform provider if they are held on some form of electronic trading platform.
I hope that helps, but let me know if you need any more information.
I hope that helps.

You should also bear in mind that once you gift your investments to your wife that you are giving up ownership of the assets. if she then decides to cash them in and spend them, its her business as they will be hers.

in terms of the notes above, it is irrelevant as to any transfer of value issues between husband and wife or civil partners as all transfers are exempt.

but although not applicable here, if you gave an investment to say your brother and you have a paper capital gain on sale, the gift to your brother is still regarded as a disposal for CGT purposes and tax will still be liable regardless of the fact that you received £0 in return.

the above transfer to your wife would be exempt but she would be regarded as acquiring the investment at the same price you did and not the value on the date of transfer. this is why taxpayers should consider the tax efficient investment options available to them, in particular ISA and pensions as for many people this is usually sufficient to safeguard themselves from unnecessary tax.

May I go slightly off-topic' here, and mention inheritance tax (IHT)? A gift to anyone other than a spouse or civil partner is regarded as a 'disposal' for IHT purposes, and the value of the gift will be counted back into the estate for inheritance tax purposes. It will drop out of the calculation and become a tax-free gift after 7 years, though.