Delete commerce line item with Ajax
Issue resolved. Having checked with Yii debug bar i could see that there was no $_post data with the request. It seems axios sends the data as JSON and not usual post data. Switching to vue-resource enabled me to post the data for craft to use, new code:

this.$http.post('', {
    [this.csrfName]: this.csrfToken,
    action: 'commerce/cart/update-cart',
    lineItems: {[id]: {'remove': 1}}
}, {
    emulateJSON: true,
    headers: {
        'X-CSRF-Token': this.csrfToken
    }
})