For example, in discrimination suits, one has the Vento scale as a guide to calculating damages. Does anything similar exist for trespass to person?
You are looking for the Judicial College Guidelines for the Assessment of General Damages in Personal Injury Cases, which had its sixteenth edition published in April 2022. This book sets out the range of compensation based on the type of injury suffered. The scale is very detailed. For example, we can find in Chapter 7,
(G) Injuries to the elbow
(a) A severely disabling injury - £39170 to £54830
(b) Less severe injuries causing impairment of function but not involving major surgery or significant disability - £15650 to £32010
(c) Moderate or minor injury
(i) Injuries fully resolving after about one year - In the region of £3530
(ii) Injuries with the majority of symptoms resolving within 18 to 24 months but with nuisance level symptoms persisting after that - In the region of £6500
(iii) Injuries recovering after three years with nuisance symptoms thereafter and/or requiring surgery - Up to £12590
There are lots of other rules about the calculations, which are beyond what can be summarised in a text box. In the case of assault, one might find reference to Chapter 4, which is on psychiatric effects including PTSD, as well as to the physical injuries. Probably the most important note is that they are Guidelines, not Rules, and so the court can deviate from them at its pleasure. But this is what the judge will have at their fingertips during the proceedings.
Because these concern damages, receipt of an award will depend on whether the respondent actually has the money. For that reason, there is a statutory scheme, the Criminal Injuries Compensation Scheme, which can make additional payments to victims of violent crime. CICS awards are reduced based on civil damages already paid, because you can't be compensated twice for the same injury. They are also calculated after any insurance payout, so it's in the nature of a final resort.
The CICS tariffs are not the same as the JCG ones. Taking the elbow example, CICS 2012 rates damage to one elbow with substantial recovery at £1500 (level A2), and with continuing significant disability at £6200 (level A7). Other eligibility rules and procedures are different as well. In practice, the majority of CICS awards are for between £1000 and £2400 (bands A1 to A4); there is a proposed simplification of the bands into fewer levels, but this has not yet been implemented.