In April 2021, the U.K. government published a very helpful report, summarised here, on achieving net zero carbon emissions that reviewed a number of Carbon offsetting projects and rating them according to a number of criteria.
A consensus is forming that carbon offsetting approaches which reduce emissions elsewhere (versus remove them) will not be scientifically compatible with true ‘net zero’ in the long term (Allen and others, 2020; Science Based Targets, 2020). However, in the short term they are still useful.
The implementation of carbon offsetting projects in the UK is less widespread than in other countries around the world. This is the result of an international carbon offsetting system that has historically prioritised carbon offsetting activities in countries across Africa, Asia, South America and North America. However, the implementation of the Paris Climate Agreement and potential changes to rules on international carbon trading, are likely to create new opportunities to implement carbon offsetting projects in the UK. This potential change to international carbon trading rules, combined with growing numbers of UK-based organisations with net zero targets, has prompted increasing interest in the potential to carbon offset in the UK.
From useful Environment Agency infographics, it looks like Upland peat restoration (which both reduces and removes GHGs) and Woodland creation (reduce GHGs) have the most indicators with good performance. Biochar (removal of GHGs) also has a good amount of good performing indicators.
What is it? Blanket bog is extensive and widespread in the wetter west and north of the UK. Generally, an upland habitat, it can be found from 1000m down to sea level where peat has accumulated to a depth of at least 0.5m – generally on flat or gently sloping ground where drainage is poor. 
England’s upland peatlands store away 138 million tonnes of carbon, equivalent to 506 million tonnes of CO2. Holding on to this carbon store is vital in the fight against climate change.
About 70% of Britain’s drinking water comes from upland catchments, which are generally peat dominated. The Peak District peatlands alone supply four million people with water. Healthy peatlands, with carpets of sphagnum mosses, provide much cleaner water than degraded ones, where the soil washes away into the water courses and greatly increases discolouration.
Today, only 4% of England’s upland deep peatlands are in good ecological condition and actively forming peat.  The National Trust and Wildlife Trust are involved in a number of peatland restoration projects across the UK:
• Peatland restoration & conservation projects | National Trust
• Peatlands – examples of our work | The Wildlife Trusts
Forestry England have a woodland creation project:
Forest Carbon leads the way in developing woodland creation and peatland restoration projects for carbon capture and ecosystem services in the UK:
Biochar is a charcoal-like substance that’s made by burning organic material from agricultural and forestry wastes (also called biomass) in a controlled process called pyrolysis. Although it looks a lot like common charcoal, biochar is produced using a specific process to reduce contamination and safely store carbon. Biochar technology shows promise in mitigating climate change and improving soil quality, as well as reducing waste and producing energy as a by product. 
The UK Biochar Research Centre (UKBRC) has led strategic, multidisciplinary investigations of biochar since 2009. It is based in the School of GeoSciences at The University of Edinburgh, in collaboration with Newcastle University and Rothamsted Research, projects include:
UK Biochar Research Centre | Projects | Complete List
The UK government website has details of projects selected for Phase 1 of the Direct air capture and greenhouse gas removal programme and these include a few biomass and biochar projects:
Projects selected for Phase 1 of the Direct air capture and greenhouse gas removal programme