For a single entry visa you do not need a letter of invitation. However, for a double entry visa you do need a letter of invitation. Visas are normally for 30 days with fixed entry and exit dates.

Application form tips

Section 11: where it asks for your educational background put your highest level of qualification, e.g. GCSE, or degree.
Section 13: Tick the “ordinary” box. “Issued by” means the issuing authority, UKPA for UK passports.
Section 14: tick the “yes” box
Section 17: write “tourism”
Section 19: List one or two major towns. E.g. Aktobe, Almaty.
Section 20: You can only enter along major roads. List the largest town nearest the border on the Kazakh side.

Section 21: Find a hotel online. You do not actually have to stay there. Usually best to find one in Almaty.
Section 24: leave blank.

Contact Details
Embassy of the Republic of Kazakhstan
Head of Mission: HE Mr Erlan Idrissov
Address: 33 Thurlowe Square
London SW7 2DS
Telephone: 020 7581 4646
020 7584 9905 Consular
Facsimile: 020 7584 8481
020 7584 9905 Consular
Email:
Office Hours: Mon-Fri: 0930-1230, 1430-1800
Visa Section: 0930-1230 (except Wed)