I would guess that many people who are not particularly religious (even many people who call themselves atheists, agnostics or humanists) know and respect the fact that we are (or have historically been) a Christian country and as such they don't want to relinquish all religious traditions.
Here are a few examples of such traditions that I can think of that are practised even by a lot of non-religious people:
Having their children baptised and having godparents
Getting married in church (or having a service of blessing after a civil wedding, which I believe the Church of England offers, or used to offer, as a compromise for divorcees who were remarrying and who weren't deemed eligible for a full church wedding. This could also be appropriate for a couple where one partner is religious and the other one isn't and would prefer a civil wedding.)
Having a religious funeral when you die (which I think is the default position for every deceased person, whether they were baptised or not, unless their family requests a different type of funeral, such as a secular funeral, or the person said in their will that that was what they wanted)
Giving things up for Lent (and having pancakes on Shrove Tuesday)
Having fish rather than meat on Fridays
Saying prayers (and/or having a moment of devotion/meditation) at bedtime and/or at mealtimes
Having a daily act of worship in school, which I believe is a legal requirement in state schools in Britain. There has been a lot of controversy over whether non-religious children (and children of different faiths) should be allowed to opt out of daily worship (and even opt out of Religious Education), though.
Celebrating Christmas and Easter (which even many members of religions other than Christianity do). Some people who aren't religious or who belong to religions other than Christianity choose not to celebrate Christmas and Easter, but that's a matter of personal choice.
Quite a lot of people who aren't particularly religious (and even some members of other religions) even go to church at Christmas and/or Easter, whether they used to be church goers or not.
Here are a few examples of such traditions that I can think of that are practised even by a lot of non-religious people:
Having their children baptised and having godparents
Getting married in church (or having a service of blessing after a civil wedding, which I believe the Church of England offers, or used to offer, as a compromise for divorcees who were remarrying and who weren't deemed eligible for a full church wedding. This could also be appropriate for a couple where one partner is religious and the other one isn't and would prefer a civil wedding.)
Having a religious funeral when you die (which I think is the default position for every deceased person, whether they were baptised or not, unless their family requests a different type of funeral, such as a secular funeral, or the person said in their will that that was what they wanted)
Giving things up for Lent (and having pancakes on Shrove Tuesday)
Having fish rather than meat on Fridays
Saying prayers (and/or having a moment of devotion/meditation) at bedtime and/or at mealtimes
Having a daily act of worship in school, which I believe is a legal requirement in state schools in Britain. There has been a lot of controversy over whether non-religious children (and children of different faiths) should be allowed to opt out of daily worship (and even opt out of Religious Education), though.
Celebrating Christmas and Easter (which even many members of religions other than Christianity do). Some people who aren't religious or who belong to religions other than Christianity choose not to celebrate Christmas and Easter, but that's a matter of personal choice.
Quite a lot of people who aren't particularly religious (and even some members of other religions) even go to church at Christmas and/or Easter, whether they used to be church goers or not.