In theory, bags labelled as 'compostable' are made from vegetable matter like potato or corn starch which fully break down. However, the conditions have to be right for them to break down and often it isn't hot enough in a home compost situation. It might need centralised composting facilities where the compost is guaranteed to reach high temperatures.
If a bag is labelled as 'home compostable' and it has been approved as compostable by the Composting Association in the UK it should bear the seedling logo.A key worry about the use of compostable packaging is that it promotes recycling, rather than reducing the amount of waste produced in the first place. It is always better to reduce and reuse than to recycle.
"Compostable coffee bags take years to breakdown whilst food and garden waste only takes six weeks at an In-Vessel Composting facility.
The only thing you can put in your food and garden bin (aside from food and garden waste) are compostable food bags with the EN1342 seedling logo on which are used to line the kitchen food caddy. These bags are made from potato starch so break down at the same rate as food and garden waste.