The payslips / P60 are evidence of income and economic activity, so you don't necessarily need your income details to be included in this letter.
As for "employment for foreseeable future" text, this may be necessary for someone applying on the basis of WP / Tier 2, but not for HSMP / Tier 1 (General) migrants.
IMHO, the following can be omitted from the text - unless your payslips / P60 have some sort of reference to this agency.
PK wrote:Mr XXXXXX receives his working assignments from his teaching agency XXXX Ltd and we facilitate his pay.
Letter from current employer - evidence of employment.
Payslips / P60 - evidence of income and economic activity in last 4/5 years.
Bank statements - evidence of salary/income credit and availability of funds (no min. income / fund requirement).
HSMP approval letter - evidence of being covered by HSMP JR.
regards